You *could* climb at full power and full mixture till your desired altitude, however you'll definitely be losing some power wasting fuel by running too rich, so the advice above is good. The approach you've given is certainly a simple method that it sounds like the school has been teaching it's PPL's.
The approach of testing full static power is an interesting one and I'm assuming not many of us would have done that before, or had to do it before, however it does seem quite valid. My only concerns though are that if you're pushing the envelope that far that you need to do this, then you may have been outside the safe and legal envelope for the aircraft performance. Or... you're panicking a little as performance had degraded not that badly, it just possibly scared you as you're not used to that level of performance. Where would you have drawn the line if you didn't get full rpm that you'd get at sea level during your static run-up?
If it's any consolation, I was listening to a couple of 172's with 3-4 pax and camping gear taking off out of the recent Mt. Beauty fly-in, heading east towards the high ground. They were both climbing and one pilot said to the other, "is your stall warning going off yet" and the other replied, "almost constantly" !!! The latter made the decision to turn around, gain some height and then clear the higher ground more safely.