First, I went back and looked at my notes on my 170 on PeeKay 2300s. The takeoff performance I quoted in my earlier post (1800 feet) were at gross alright, but with a "student" flying the plane...ie: someone working toward a SES rating, with very little float experience. That airplane at gross with someone experienced flying it got airborne in 1000 to 1200 feet.
Would a 180 with the PPonk conversion get airborne sooner? Oh, yes....no doubt. That is indeed a great conversion, and fuel flows CAN be as stock if you learn to keep the throttle back in cruise.
Things to consider in any of these airplanes:
Float kit: VERY few 172 came with a float kit. Not that many 170s came with a float kit. A larger proportion of 180s came with a float kit, but still less than half, I'd guess.
Adding a float kit: It is possible and maybe even practical to add a float kit to a 172 or 170. It is NOT practical to add a float kit to a 180, in fact not even close. For starters, the belly skins have to be doubled under the cockpit area. Now, as a caveat, I believe that the 53 model 180 can be converted similarly to the 170 (the fuselages were similar if not virtually identical). BUT, an important consideration in this kind of decision is that a key component of factory float kits on 170/172/180 airplanes is factory corrosion proofing. And in those days, when Cessna corrosion proofed an airframe, they did a really good job. An old friend who worked for Cessna in those days told me they zinc chromated the skins before assy, then shot rivets "wet" with chromate......a messy proposition. The non float equipped airframes had no or little internal corrosion proofing.
Fuel tank capacity: As you describe your mission, it's very much like many of the missions I flew in my working days: A fair distance from home, with weather always a potential, meaning frequent diversions.....eating more fuel than planned. There are a couple ways to deal with his, and I've done them all at one time or another: Tanker fuel in long range tanks, leaving home or the nearest fuel stop to your hunting area with full fuel, giving you the range to get to the hunt, then get home. That works, maybe, but now you REALLY need the takeoff performance (and the useful load, of course) to make it work out of that mountain lake. OR, with some prior planning (perhaps during a scouting trip of your hunting area, cache some gas in cans on a larger/lower elevation lake. In addition, you may wish to use that larger lake as a staging point to shuttle your partner/gear/dead animals out of that high lake. For a lot of years, I used shuttles to move big loads out of small lakes in northern Alaska, and I had gas caches behind many bushes on those lakes. I would point out that this is a LOT cheaper than bigger, more powerful planes/engines. Consider that bears can be pesky, but in twenty years of caching gas cans in dense bear areas, I never lost a can to bears. Some mysteriously disappeared, mind you....
There is no doubt the 180 is faster and more fuel efficient than either the 170 or 172. And, it will probably carry more.....depending on model year. Beware the up-gross kits, or at least the use of those higher weights, for you're going to impact performance......but you could use that feature to tanker fuel from home....
The early 180s are the lightest, but are excluded from many of the attractive mods, and they have small fuel tanks. Look at all your possibilities before dropping cash.
I question the prices noted earlier, comparing 180s to 172 and 170s. The big engine 172/170 do indeed bring a premium price, but so do "decent condition" 180s. Look at the airplane sales outfits, and you'll indeed find relatively "cheap" 180s, but take a close look at those, and I'd bet that 99 out of 100 you'll run not walk away from.
Best of luck, but for my money, I'd look for a good solid plane on good floats, and plan to shuttle. At that altitude, seaplane performance is really impaired, whatever you're flying.
MTV