It's really a non-event going to 10,000 feet in a Warrior. I flew them through my PPL training, and the only time I didn't get above 8500 were on city scenic flights.
Yeah, it takes a long time, particularly if its a 140hp puppy, but if you're going a long way, the higher TAS up there makes it worth while. (Check the winds, though).
In a few of my previous jobs, I was taking 182s to 10, 12, and 14,000 feet many times a day... provided you keep the engine warm, the descents are where you can have fun. Spiral-diving at 4000ft/min is a very entertaining way to get back to the ground again...
Doing it in a turbine makes life so much easier, when you don't have to worry about engine cooling - close the throttle, point the nose at the ground, and don't exceed V
NE.
The thing that almost made my heart stop, was the comment on holding a pilot's license, but having never actually leaned the mixture
To me it beggars belief that someone could actually train a pilot and think that it was somehow acceptable to not lean! (this is a comment on your instructor, not you)