I didn't mention the starter bolts but Super Samuri did. But, Yea' you may have to use longer ones to get them started and then switch to shorter ones. Thats totally normal, standard procedure.
I'm reluctant to mention it as I don't want to sound like a smart ass or know it all, but be carefull. When you calculate the air pressure times the surface area of the sidewall, there is literally tons of force trying to blow that ring off. I would make sure every bolt is perfect, none that are bottomed out, cracked or over torqued ect.
Im sure you already know this, but I know there is some young guys on the forum who dont, but, up until the early seventies the old 16.5 rims used a spit rim with this lock ring that held the outer rim flange on: the wheel split in two. The tire mechanic had to pry the lock ring off, dismount the tire and replace the rim flange and lock ring. If the lock ring wasn't locked perfectly in the slot of the rim, then as the tire was inflated, the sidewall would blow the lockring and rim flange off with explosive force. This has killed lots and lots of people. I believe split rims were finally outlawed for DOT use. I'll bet You-Tube has safety videos of this kind of failure.
If enough bolts are missing, broken or otherwise bad on a beadlock ring I suspect the same thing can happen. When you talk about breaking bolts off your worring me.
EDIT: I did a little math to calculate the force on a bead lock ring bolt flange. I came up with 6511 lbs (three tons).
Warning; boring math below:
Based on a 37" tire, 15" rim at 25 psi:
Surface area of a 37" disk (tire shadow) Pi x radius squared= 1075 sq in.
Surface area of 15" disk (rim area) same formula as above= 177 sq in.
Tire shadow surface minus rim surface equals actual sidewall surface area= 898 sq in.
Multiply by 25 psi times sidewall area and you have a force on the sidewall of 22,450 lbs.
116 linear inches (71% / 15940 lbs) of this load is restrained by the tire perimeter and carried to the opposite side of tire, 47 linear inches (29% / 6511 lbs) , is loaded on the beadlock bold flange.