Not sure about that particular pump since they changed them a couple of years ago but the cast iron version of that one was a darn good pump for the price, I know of two of them that have been in service about 3 years and are performing well. For sure you will need the 13 HP to run that one because 6.5 would not be near powerful enough, you need over twice the power rating when using a gas engine vs an electric motor and three times the power rating is not too much!
Just an idea here, how about using an electric clutch controlled by a regular compressor pressure switch? You would still need an electric throttle kick-down and you would need to sync the throttle and clutch but that should be doable. Not sure how the clutch/engine would handle the sudden jolt of engaging such a heavy load as that compressor pump but if you use the unloader valve that's normally used with the pressure switch in conjunction with the tank check valve the the pump would be unloaded when starting, just a thought.