Go ahead, try the 40 amp ... especially if you have good voltage and a short run. "Maximum" means just that; nothing wrong with a smaller breaker.
Ditto for wire size. Run #8 if it makes you feel better.
"Heat pump" is a bit of a misnomer. Think 'air conditioner,' and not 'pump.'
I'd also look to see if the unit has an auxillary heater in it.
