You are correct that the thrust-to-waste-heat ratio is higher.
But the engine runs hotter because more is actually burned.
Don’t know about the burn efficiency. I know the supersonic burn front has major implications, but conflagration vs detonation and what isn’t burned? Haven’t looked at it.
I do know the engine is smaller so what waste heat there is has less area. Like I said, real world... no clue. Its like communism. In theory and for ants it works great. Real world, not so much.
Physics says less waste heat.