Normally, we like to take advantage of fear and stress in a new rat to help inspire it to bond with us for safety and security.
Look at it this way: You're lost in an arctic wilderness in a snow storm surrounded by wolves and a big friendly Grizzly Bear comes along chases off the wolves and huddles with you to keep you warm... You may not be a big bear fan, but more than likely you've just made a giant new friend. But what if you were so terrified you couldn't wrap your head around the bear being friendly, not so much because you are terrified of it, which you may very well be, but because you're freaked out about everything and just in a panic.
In immersion and in shoulder rat training, fear can be your friend while panic is always your enemy...
We're not just trying to reduce the stimuli, but I'm thinking we're giving the rat a safe place under the blanket to relax with you... The idea is to reduce her natural agoraphobia. Imagine if you could get into Olallie's igloo or rat house with her and make friends there, you're just too big to fit, so you're making a bigger igloo or rather tepee. Someplace warm and cozy where she can relax a bit and get to meet you... A giant womb if you will... She's still going to fearful, but hopefully not to the point of uncontrolled panic. And under the covers you can show her you are the friendly bear.
It's more than just reducing stimuli, it's managing fear and introducing yourself as someone safe in a safer place...
Oddly skittish rats don't just learn to trust you over time... because you don't have any meaningful contact or communication, nothing ever improves... days turn into weeks and then into months and you spend your time in perpetual stalemate or groundhog day, all over again. The longer this stalemate goes on, the more it becomes the "norm" and normal is good for a skittish rat, in any case the rat feels it's better than "worse". And the normal becomes harder and harder to change.
As to biting, this morning I've been "bitten" at least 100 times by Misty. She mock bites and attacks me because she's playful and also it's a meaningful communication for her. She mock bites and mock attacks, I mock defend myself and eventually she flips over and I skritch her belly and then she licks me and grooms my fingers... we do this every morning and several times after that. It's a ritual. It's her way of saying good morning or hello. Now when my neighbor grabbed my part wild rat, his hand and forearm sprouted fountains of blood almost instantly, I suppose it looked a lot like Misty play fighting, except a lot faster, but this wasn't any friendly greeting ritual. This was full on survival aggression and the blood soaked towel around his hand and forearm made it pretty clear that this was no game. That rat turned from the sweetest thing to full on vicious on a dime. And she went for the face and eyes first if she could get at them, even when play fighting. She let my 5 year old daughter stuff her into doll clothing, but for me, she was handled with kit gloves and she loved me, just not as much.
Most rat nipping or biting is somewhere in between those two extremes... A rat might tell you "lets play" with lots of gentle little play chases, and mock bites, or it might be warning you to back off with a firmer nip, or it might be telling you it's in charge by attacking you and trying to get you to submit (as in hormonal aggression), or if it's cornered it may be self defense biting like when our part wild rat defended herself against my neighbor. He grabbed her, not realizing she was part wild... she looked a lot like Fuzzy Rat who he knew was sweet and safe, and she went into full on wild rat survival mode.
It's hard to know for sure why your rat is biting... it sounds like it's a warning to back away, which is better than survival mode panic biting by a long shot but not nearly as good as friendly and playful mock biting for the sake of greeting and bonding. I'd say that how hard you're getting bitten can give you some clues. But I'm thinking, my neighbor didn't need quite so many and such painful clues and neither do most of us, so it's a reality that can be hard to test.
If Olallie is biting when cornered, it's defensive survival biting, if she's gently nipping when she's got plenty of running room, it can be a greeting or it might be leave me alone... that's hard to tell.
As long as the biting or nipping is playful and painless, I always play along. But when it hurts, I don't squeak, I shout and bop... No, I don't bop to hurt or punish a rat.. but I am communicating that biting is wrong. I'm not looking for empathy or to try and make my rat feel bad because she hurt me... I'm saying "No way, no how! Never and Not Ever!" Everything I communicate to my rats is that I'm their friend and that I love them, but when they bite or nip too hard, they get an immediate reminder that I'm also the bear in the room... I may be the nice bear and they know I'm a super soft touch and that with a little persistence they are going to get most of my pecan pie, but they also learn that biting is the one thing that is going to make me very angry and no one likes it when I'm angry. Oddly, when I do bop a rat, which is so very rare, they almost immediately come to me to apologize. They give me lots of kisses and licks to basically say that they are sorry and "lets be friends". They don't think I'm evil or terrifying, they know they have done wrong... So yell and bop if necessary it isn't so much punishment as it is communication, with all communication there is a reply which is the I'm sorry phase to which I reply by giving them lots of snuggles and skritches and hugs...
Now as Olallie isn't bonded to you properly, you run more of a risk of her getting more fearful when you enforce your no biting policy, so try and be a little bit more gentle at first... Try a loud NO BITING! first... But don't play submissive rat, be the bear. I know, you really don't want to be the bear, but as long as she is biting you it's hard for you to be the "nice bear". And as she's already afraid of you and sees you as the bear anyway, there's likely to be no or very little harm done to the relationship you don't have in the first place.
So in short, nipping and biting can have several meanings, it's rat communication to which you need to reply... Try to determine what your rat is saying and reply appropriately. I'd love to make the call for you as to what she's saying, but I can only reply to the way you see things. I'm looking through your eyes and interpreting your words which may or may not be accurate... so you need to do the assessment yourself as you see it on the fly. She may be biting for different reasons at different times.. because you are hands on, it's got to be your call.
Odds are that Olallie may have been mistreated or even abused as a pup, she may have been taken away from her mom too young and just neglected... Since we have had Misty we've spent many hours each day with her holding her and playing with her and napping with her and in general replacing the love she should be getting from her mom... and she's still a bit skittish. She's napping on my desk right next to me now. We had to go backwards (under the blanket) in order to move forwards. But the goal for now is always the same; to build a bond based on communication and understanding and eventually trust. We are socializing her into our family, building her confidence and making sure she understands we are safety and comfort and her forever family. I just had to stop for a 5 minute skritch and lick session with her... in which I kept repeating "Misty's a good girl" which will come to be her reward phrase when she gets older. Reward phrases work better than treats.
In any case, you adopted a problem rat, over time the problem has become the norm and you have to do something to get out of groundhog day. Olallie is going to resist change and it's going to be traumatic no matter what you do... the blanket corollary works a treat with terrified new pups, so it 'should' work with some older terrified rats too... Normally with thousand of immersions done worldwide, I can pretty much tell someone how something will work with a good level of certainty, but I really can't see any harm to your current situation and my best guess is that this should work if you can get Olallie to come under the covers with you.. Try and find a blanket that will be dark and cozy underneath.
Best luck and keep me posted.