So, as I can't currently put it on a rack, I left it lying on its back last night on a cotton t-shirt, as I have many times so far in this build. The same T-shirt that has proven an effective bed even when applying a fair bit of sand-and-polish pressure to the front.
And as I lifted it up this morning, up came the t-shirt as well.
Head. Desk. Interface.
I don't know if it's the heat or what but I think I'm just going to pop the neck off again and leave it hanging for a month.
I can build up the solder divot and the polish through, and the stand marks, in the meantime but I'm not going to let it touch ANYTHING until the end of September!