I have some of the Kaiser 11"-14" Barbie type stands but their waist rings are just too loose to grab the dolls. I had to order them for my 1:6 stuff and got some spares in the order. Some of their other stand might grab better, but Kaiser uses one base for all their stands, so a ring that might work may be too short to put into the stand. But if you can find a stand that works well you could also mount tiny neodymium magnets into the shoes to stick to the metal base(I know Abbey's shoes have pegs, drilling small holes might not be too much trouble)
I checked Justice to try to order Toralei today and they look to already be out of stock.