Looking at the photo, there appears to be a fair bit of height in the viv, do you know the dimensions? I would suggest looking at a way to raised the level of the basking area a bit to try and improve it, but I actually get why kitchen towel is going to be better here.
There are two ways to take temperature readings that are talked about with setups for reptiles, some use surface temperatures, other take ambient (air) temperatures, and I see Murri has mentioned getting a temp gun, I highly recommend it as well. The basking temp surface should be around 110f to 115f, the air temps then around that would be a little lower normally and then you want air temps around 75f in the far cool side/under shade.
I understand that he has had issues in the past and he is also on a vet care routine, so theres long term effects from how sick he was. I wouldnt change from anything the vet is telling you to do and I wouldnt use a substrate here.
I think you are on kitchen towel and easy to clean slate with him for the rest of the time you have him (also considering your own illness/situation and you say you cant really deal with much more than what the current tiles are), and thats probably the best given the situation.
I would look at the guard you have on the basking lamp you have, and depending on the height of the viv, see if theres a way to perhaps lower that basking lamp? I would change the guard for a dome regardless, try and improve that basking area a little. Raise the basking area or replace it with something with more height to it. You dont need the guard, theres no way he'll reach that in the setup you have, even if you did have less distance in bulb to basking it would have to be a big change in that gap for the beardy to be close enough to get to the bulb. Theres nothing within reach of it in your photo and beardies cant jump up to get to it.
The CHE, is set to 75 at night did you say? i would drop that to 65f/18C (i dont use one at all for mine, but house temp is around 18C at night anyway, Scotland is going to be colder i know, but you still want to aim for about 18c, you dont need it as high as 75f (24c) at night). I would try to look at a way to put something more of a cave/hide in though, he really does need a refuge space and the pics look like its all very open and exposed.
In a standard setup it is true that you want around 40% in the cool end, but, I dont think humidity may be as big an issue as it could be in this particular case. You say you let him out a lot and he is very active, outside of the viv (and going off your name) the humidity is going to be around 40% if not a little higher in scotland. You mention a ramp for the windowsill for example, is he almost free-roaming during the day then?
Your setup certainly isnt what I would recommend to someone, but that would be with a healthy beardie, and assuming an able bodied person, so its a little different here. I think a few little tweeks as mentioned, but the sterile type approach to the viv is likely safer for him and easier for you to manage and the most fitting to the situation. If he has got that free access to move out into a more humid environment (IE your house, rather than the viv) then that would be addressing his need for a little more humid retreat type area (which would normally be their burrow in the wild)
I havent seen if you managed to get the video up to show what you mean regarding a twitch, is it constant or just the occational one off flick when dozing or sleeping? You say its fine when he is up and active.
Ask you vet about what actual tests he does, if he is doing tests such as bloodwork, D3 may already be on the checklist. Should be as easy as a phonecall to find out. Twitches can be from mineral imbalances, so its certainly possible as a cause for concern here, especially with the history. As you said the 6 month check are required, so the vet recognises the fact theres going to be long term (possibly lifelong) fall out from before.