I can't speak on the Conquest II directly. I flew an MU-2 Marquise with the -10 engines. You do have -10 engines right?
Good engine. Powerful, reliable, and very efficient. Starting and stopping the engines is a practiced procedure due to NTS checks and putting props on start locks.
In the MU-2 I would see as low as 230pph per side on a good day in the upper 20s. I think the Conquest is a better climber so you may see lower fuel flows, but only if you are RVSM. Planned on 100 gal the first hour, then down to 80 per hour after. In Marquise I saw 280-305 TAS
Have fun, sounds like a fun plane