A typical case of someone (the other guy) trying to do you a favor, but, in dragging his feet, ends up causing more confusion than help.
Considering the part itself did not cost you anything, I would either give it another day or 2 or source another part from a more reliable source like a watch parts seller.
I am unfamiliar with an SOA44, but check the threads on both the tube & inside the crown to see if they are cross-threaded or otherwise damaged.
If both are ok, then either the stem may have become dislodged or the keyless works are misaligned (you will need to remove the movement from the case & the dial/handset to check this). If unsure or you lack the requisite skills/tools, this is definitely something to let a pro take care of.
I think I would wait until you have unpacked everything before losing your grip. Moving, as you correctly stated, is very unsettling & you probably had a dozen things going through your mind when you packed your watches (without thinking) into what seemed to be a logical place. Unless you transported your watch cases loosely, so handymen would be handling them directly, I would not worry about them. I am sure they will turn up.
The general axiom is - you break it, you own it. Considering the condition, unless the damage was accidental (& you feel like doing the customer a favor), I would happily offer a replacement at full price or the option to smear away.
Ditto most of the above. The Minh dial's a poor copy & the NDT (as well as any other aftermarket dial) will be a step down from a damaged gen dial.
Were it mine, I would start looking for a used gen dial. A local Rolex watchmaker, ebay, TZ, VRF or other gen sites are your best sources.