Rather than 'park' you should pop it into neutral and apply handbrake - as you would on a manual if you take your foot off the clutch.
The whole drive chain 'shunt' will disappear then as 'park' locks up the system, which I think is what you are experiencing, as you are asking the car to 'park' and then 'un-park' on a gradient. Park should only be used when, bizarrely enough, parking I think...and engine turned off.
Neutral is there for just the type of situation you are describing - depress button and move to N, then when ready to go, without needing to press the gearshift button again, simply flick into drive without any winding up of the whole system and off you go. Test handbrake/hill start procedure the first couple of times though to avoid roll back.
Dave