How to organize multiple electrical wires going into an ultra thin recessed light?
Use an old work box to house the splices

There's a simple way out of this, and that's to use an old work box mounted into the ceiling drywall to house the electrical splices.  A 3 gang switch box will do the trick, or you can use a 4 11/16" square box that's 1.5" or deeper if you can get an old work mountable version of that.  (Really, anything that supplies more than 29.5 in3 of space will do.)