When I was instructing out of Laramie (elev. 7277'), most of it was in 172s of various vintage, including 145hp Continentals, and 150hp and 160hp Lycomings. Our "instrument trainer" was a 182, and we had 2 other 182s that we did some instructing in, but mostly that was for people transitioning to the larger, more powerful airplanes. So I spent a lot of time in 172s at high DAs.
With only 2 reasonably sized people aboard, a properly leaned 172 works very, very well up to DAs into the 11,000' range. It'll definitely go higher, but it's a strain. Put a person (or equivalent weight) in the backseat, and performance drops off significantly, but we did a lot of training with 3 aboard, the student, the instructor, and typically another student watching. But you just have to get used to the anemic climb performance.
A couple of illustrative stories about 172s and high DAs:
First story: My step-bro and his wife were visiting, and Wife 1 and I wanted to show them the Laramie Valley from the air. He was a newly minted private pilot, learning in a PA-28-140 in the Detroit area, where airport elevations are roughly +/- 700' MSL. It was a very warm day, about 85F, so I'd made a point of making sure that the airplane had only half tanks. With our respective weights of about me at 170 (that was 30 lbs ago), him at 160, Wife 1 at 130, and his wife at about 120, nothing in the way of baggage, and approximately 130 lbs of fuel, we were actually about 120 lbs below gross. When I called FSS for a field advisory, I got the usual comment, "Caution, density altitude is approximately 10,500'."
As I did the run-up, my step-bro asked "why are you doing that?" I replied that at higher density altitudes, it's necessary to lean the carburetor for the elevation. OK. Then we taxied out to 21, and our take off roll was something like 3500' long. We broke ground right about where 12/30 crosses 21/3 and climbed out at the rate of about 250 fpm. He then asked, "what's wrong with the airplane? Shouldn't it climb better than this?" Again I explained about DA, and how it affected power, lift, and thrust, and that this was as good as any 172 could do. We continued to climb out, flew around for awhile at around 10,000', which was just about what the airplane could do comfortably, and then returned. It was quite an eye-opener for him.
Second story: One nice summer day, a young couple and their two little girls landed at Laramie for fuel and lunch in a shiny new-looking 172. This was in the late 70s, so it was probably a 160hp model. I don't recall where they were from, but my recollection is that it was somewhere in eastern Iowa. They borrowed a car, drove into town, and returned. He did a pretty thorough preflight, they loaded up, and they taxied out. From the black smoke coming from the exhaust, it was obvious that he wasn't leaning for taxi. I watched him do the run-up and pull out onto the runway to take off. A few minutes later, they taxied back in. He had aborted the take off, and he said as he came into the FBO office, "There's something wrong with the airplane. Is there a mechanic around?"
I told him that since it was the weekend, there wasn't any mechanic, but I asked him what was wrong, and he said that it didn't have any power. I asked him if he'd leaned for take off, and I got that deer-in-the-headlights look that said, "I don't know what you're talking about." So I offered to show him, and he was really aghast--"the manual says full rich for take off!" I assured him that at Laramie's elevation, no matter what time of year, we always leaned on the ground for best power. I also cautioned him to expect a much longer ground roll and a relatively low climb rate compared to what he was used to. So they loaded up again, and this time their take off was satisfactory.
I have many more stories, but let me end with this one. I was having lunch at the restaurant at KGXY (Greeley) and overheard a discussion in the next booth. An instructor and his student were planning to fly into Marble, CO, the next weekend, in a stock 160hp 172. The instructor, from the Denver area, was accustomed to high DAs, but he'd not flown into the mountains in one. I was going there myself that next weekend, so I made some route suggestions. As it happened, on the day we flew in, they were ahead of me, announcing over Redstone as I entered the canyon south of Carbondale. I heard their announcements, and as I was on upwind, they announced downwind, and there they were. But as I turned downwind, they announced that they were going around. I landed, and soon afterwards, they landed, also.
I helped them park, and I asked the instructor about the go around. He said that his student had misjudged and was likely to land too far down the strip, so he had told him to go around--always a good decision when things don't look right, even if the landing can be salvaged. I asked him how the airplane had performed, and he told me that the only issue that they'd had was coming over Corona Pass, because the climb rate had dropped to about 150 fpm for awhile, so that they had circled to get up to 13,000' before crossing. They had kept it light--didn't even bring a tent! Here I was with my full "glamping" equipment (large tent, cot, chairs, cooler, 35# survival kit, 67# dog and her needs, etc.). My P172D has 180hp and a CS prop, but I'll bet as light as they were, their airplane performed better than mine did.
One last thought: Your STOL kit and VGs won't make any difference at all in your airplane's abilities at high DAs. They do slightly lower your stall speeds, and they give you more control at slower airspeeds, but they don't work miracles. You're accustomed to airfields of around +/- 3000' MSL, and there's a big difference in higher elevation airports. But take it easy, don't expect too much of your airplane, and it'll be able to handle the mountains. I strongly suggest that you get some mountain instruction, though--it's worth its weight in gold. When you're flying at the edge of your airplane's performance, and there are rocks on either side of your flight path, it can be pretty daunting.
Cary