Rick this doesn't make sense for all the symptoms you described!
When the weight comes off the nose wheel the strut extends (or drops) to it's maximum, and the squat switch allows the gear to move...the same thing happens whether the strut is over OR under inflated! So merely changing the inflation of the strut will make no difference to whether the squat switch stops retraction (unless there is zero strut pressure and you're inverted when you retract the gear - or like Larry there wasn't enough pressure to extend the strut far enough to activate the squat switch).
I discounted the thought that your problem lies in the squat switch because a faulty squat switch will allow the gear doors to open, but not allow the gear to move - your description of the gear half way retracted gear doesn't fit that description.
However with a faulty squat switch, the green light staying on would be correct (the gear won't move) and the pump would continue to cycle after opening the doors, eventually shutting down due to overtemperature or popping the circuit breaker (also similar to your description).
Are you SURE the undercarriage was trailing (with the green light still on)?
Even if the squat switch proves to be faulty (I hope it does, because it would work out much cheaper to fix), changing the strut inflation is unlikely to fix it - you'd have to replace the switch or the mechanical device used to activate it.
I'm keen to hear the further details from the shop when you pick the plane up. I would also operate very carefully when you do fly it, because if all they did was service the strut, then I don't think your problem is solved!
These gear problems can be real bears - I've experienced several that magically go away when the aircraft is up on jacks, and then reappear intermittently in the air. Unless you find a smoking gun, I'd assume that it isn't solved.
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