Not sure that you want to apply lubricant to the tire bead. Most of the things you put on tires and rims to mount them lubricate while wet, then dry. This gives you a good frictionally stable joint. Silicon grease doesn't dry, nor does it wash off (ask anyone who's tried to paint a Silicon grease-contaminated frame).
My next kvetch (
) is the broken bead. If the bead cord is truly cut or broken, there is no glue that can fix it. Kevlar can have a tensile strength of half a million psi. Epoxy has a tensile strength of 3500 psi or so.
If the bead is broken, and the grease lubricates the bead sliding, it could fail catastrophically. Let us know if it holds, but I'd be very leary (as in, I wouldn't do it) of riding at speed with a grease-lubricated tire with a broken bead.
BTW, silicon grease is compatible with most rubbers (not fluorosilicone or silicon rubber). So that's perhaps a little bit of relief.