My advice is to find a way to let your rats come out themselves in a small rat proof area. I use a playpen for this, and velco it to my cage. Then I can just pop open one door, and my rats then get to choose when to come out and when to go back. This does a lot to increase their confidence because they know they can always go back to their ultimate safe spot (the cage), and as a result they warm up to free-rang faster. This also prevents free-range time from being poisoned with the fear of handling - in the past I accidentally did that to a few shy rats, pushing handling on them to get them out for free-range, and it would take them a good 15+ minutes to stop hiding and start walking around. Of course this did nothing to endear me or free-range to them and in fact both those girls started to react accordingly when free-range time came around - where they would usually approach the cage door for treats, around free-range times they would actually run away from the cage door if they saw me! It was heartbreaking and at that point I realized I had to take a step back - for those 2 girls I had a different setup and so painstakingly worked for 30+ minutes daily to get them hopping onto my hand for treats, then when they did so without hesitation would take them to free-range.
And this worked, but it took such a long time and put so much stress on us both (because I wanted to make the most of the free-range time I could give them and I had other rats who readily came out, making it a juggle between them). So with my next set of rats I changed it - I added velcro to my free-range playpen, velcro to my cage, and attached them. So I could then open the door and let the rats decide to come out and go back on their own time, and they wouldn't associate handling fears with free-range itself (plus my confident rats could make the most of the entire free-range time).
And this worked great! All of those skittish rats warmed up to free-range in just a day or two, and from the start found it highly rewarding. I was then able to feed them liquid treats when they approached me, and they could climb on me or under my blanket and just start interacting with me on their own terms.
Since then I've used this method of free-range for all my rats and they have all loved it. Its also great for me because they return to the cage automatically to pee/poop (they still mark some of course, but they do anything else in the cage). they also have access to food and water inside, and are much less nervous from the start in general. So I would highly recommend this version of free-range where the rats get to decide - and the benefit of using a playpen like I do is that it contains the rats away from furniture, so its easy to get them back in the cage even if they do get spooked (otherwise I use a noisy jar to hold treats so they learn to associate it with treats from the start - I do also teach a formal come call later on, but shaking my treat jar works as a extremely effective backup that has even my shyest rats running to me right away because its been so highly reinforced).
On top of all that I would recommend LOTS of houses, huts, and other hides in the free-range area - rats are prey animals after all, so they are scared of open space, and prefer to stick to corners and hides when in a new environment. Once they adjust they won't mind the open space, but until then you want to help them adapt quicker by making it as easy as possible with many hides (I also recommend wearing a blanket or hoody because rats are burrowing animals and so feel safe when inside a dark, warm, enclosed environment - so this attracts them to you, and helps to make you out as a safe spot).
As for handling I would keep up what you are doing - some rats will do find if you force handling, and if a rat is medium confident or more I find it can even speed how fast they adjust. But super shy rats simply can't adjust and will shut down if pushed too hard, so for them you want to take it slow, and work to gradually increase their trust levels (and honestly I now favor this for all my rats regardless - even the most confident rat can benefit from being given the choice to choose to be handled, and so I like to teach all my rats to willingly hop onto my hand for treats and later transportation in order to make it both a choice for them to make and also to make it extremely reinforcing to choose to make that choice.)
For now I wouldn't pet them if they are already nervous eating liquid treats on your hand, but once they hop on readily and don't feel tense like they are wanting to back off at the same time then you can add some petting and hand motion - some rats will never love handling, and some of mine (including my current oldest girl Sugar) never learn to like it. But by teaching them to come to you and hop onto your hand when offered you will have a guaranteed way to transport them easily regardless, and as a bonus it will also teach them to be more confident because they are making that choice to approach you instead of the other way around.
(As for your vacation I wouldn't worry - rats don't typically regress with any trust formed through positive interactions, and while they may be a bit wary for the first day when you get back due to the change in schedule throwing them off, they should settle right back soon after that.