I've flown 172s with all the types of flap switches mentioned and the "spring loaded flap switch" is my least favourite.
I don't think I've done a full-flap overshoot since my original checkout and I don't remember what we did. It was £10 an hour dual, so you can imagine why I might have forgotten!
To answer shumway76's question, if I was confronted with that situation either on the ground or in the air, I would apply full power first and then hold the flap switch up for five seconds, while at the same time, remembering to push with my left hand to maintain a proper attitude. Then re-trim.
This of course assumes that the throttle friction is behaving properly. I know students are taught to keep their hands on the throttle during takeoff, but if there is another more important control to operate, then switch to that.
In my glider towing days, I would routinely move my hand after full-power was set and hold a fuselage tube immediately adjacent to the tow release. A much more important control under the circumstances and I've never had a throttle roll-back in nearly 1000 tows in Scouts, Citabrias and 182s.
I agree with PilotDAR's comments about full-flaps. Always use them where possible and "with appropriate skill" even in strong crosswinds.