[HiJinx]

Would it be feasible to re-bore the M4 and M16 to use 7.62mm?

That's called the AR-10.

[DMZFrank]

Not without a complete redesign of the upper reciever. The chamber pressures are too high. For example, the Belium FN-FAL was origionally designed for a smaller round than the 7.62 mm for which it was rechambered after NATO adopted that round. It's design is at the limit for that round.