and "recessed" ?.......and you've tried a good socket wrench ?.....or impact wrench.........a bolt 5/16" is pretty small and will usually twist-off and break with little effort......
What about the other end of the bolt.....The "nut" is usually easier than the "head"....
"Liquid Wrench" or any of the many quality penetrating oils......and some time......Hammer 'shock' them.......
All steel construction ?.....heat is your friend........
Cutting:
if it was One and not 50 I would suggest a "dremel" and an abrasive cutting wheel........
.....would any grinder fit.......
a "nut breaker" is available but may not fit the small opening.....