There's no challenge getting a UK vat number after you pass︄ the threshold. And without one you wouldn't charge vat so the client wouldn't need to︅ deduct it. And a US llc can't easily get a EU vat id, so I︆ don't understand why you don't use that argument against a US llc also.
If brexit︇ happens you will not charge vat to a non uk client.
Apart from this, a︈ lot of the discussion here refers to the actual laws and the facts on where︉ you are or might be tax resident. If you don't want to ask your local︊ tax office if you are tax resident there, then a lot of the advice here︋ might not be precise. If the main goal is to not get caught then the︌ options you have is different vs if you try to make a long term legal︍ solution that will stand if anyone should question it.
If brexit︇ happens you will not charge vat to a non uk client.
Apart from this, a︈ lot of the discussion here refers to the actual laws and the facts on where︉ you are or might be tax resident. If you don't want to ask your local︊ tax office if you are tax resident there, then a lot of the advice here︋ might not be precise. If the main goal is to not get caught then the︌ options you have is different vs if you try to make a long term legal︍ solution that will stand if anyone should question it.