DAP Rapid Fuse is a slower curing super glue. It allows you to reposition for about 30’seconds then it sets.
Get the small squeeze tubes instead of the bottle for more precision. There’s also a bottle with a brush.
Lowes and Home Depot has it.
It’s a sad commentary on my life but I have 35 years of adhesive expertise.
Modeling clay as internal support structure is a great idea. Because of the slow set time with rapid fuse, you can also apply a small amount to the clay who I will give more surface area to bond to.