First of all, I would have to agree that you make a good point on post #107. Given HR letter and transfer instruction letter are out of question, if you can provide such documentation you mentioned on the post [perhaps the most important one will be the utility bill], it will very likely defeats the UK residency permit [as I'll assume you're yet to have one]. How possible is it to procure utility bill not only until 10th June [where this situation began] but to the date far beyond it, like July's bill perhaps? It'll rather more definitively shows that you're still here in LUX even after the situation.

Next, your draft, it's nicely written, and what I suggested might sound superfluous, but the idea I have in my mind is to "raise" your "bet" with Rollbit's staff who handle this case to a point he has to "check" [forgive the terms]. They probably already will reconsider to let you perform enhanced KYC with those documents you offered you'll provide, but what about raising the bet by to a point they're question their position by telling them that you're more than willing to do a video KYC at a random time [clearly should be done on LUX timezone, and at the time you'll likely to be available, so at 23:00 is clearly out of the table] at one or two hours notice?

So they don't have to give you the schedule ahead of time [this is what usually happen for a video verification, they give the date and time far ahead]. Rather, it's at one or two hours notice, of which you'll also offer to take the video call with LUX landmark being visible [perhaps a simple restaurant sign, street sign, billboard, or other thing that clearly shows you're in LUX]. I believe they'll have to agree that such feast is rather impossible if you currently resides in UK, to arrange a flight, buy a ticket, board, fly, land, and drive to a visible sign of LUX within two hours, not to mention clearing the immigration.

If I were the officer tasked to handle your case, I think I'll seriously consider your living situation in UK if you dared to provide such arrangement. The downside of this will be that you have to constantly monitor your email, waiting for their invitation, as the window is very narrow.