First, let me state that I have zero experience with Zenith airplanes, other than watching them takeoo and land a few times.....
But, as Cary said, floats significantly and negatively effect the performance of any airplane. Amphibs are worse, simply because the floats are heavier than straight floats.....usually substantially heavier.
Now, add density altitude to that loss of performance, and you may have a plane that can land on that 5800 msl lake, but it can't take off. My only argument with Carys points is that the hypothetical takeoff scenario his examiner offered might in fact be a case where that airplane, on those floats, that day may not have been able to take off, period....no matter how much lake was available.
Float design, propeller performance, and wing design all play a MUCH larger role in launching a seaplane than they do on wheels.
An example: For nearly a year I was assigned a Cessna 185 on PeeKay 3500 B amphibious floats. These early PeeKays were hell for stout, but water takeoff performance was pretty bad. One day I landed in an ocean bay. Two aboard and 70 gallons or so of gas and survival gear.....light load. When I went to take off, a mile wasn't enough, but I had the whole Pacific, so I set sail for Hawaii, looking for a wave to bounce the thing off, which finally got us airborne. This was true glassy water, and those floats simply weren't inclined to go flying that day.
And, as Sidewinder pointed out, Amphibs on wheels can be hard on an airframe, but much of the abuse there comes from water work....remember, floats generally have no shock absorbers, so any wave action transmits a lot of forces right up the struts to the airframe.
Again, I know little about the Zeniths, but I can tell you that the density altitudes you're describing would be VERY challenging for any seaplane, even the highest performance ones around. Density altitude REALLY has a negative affect on seaplanes. The reason is that, for the airplane to take off, the wing has to accelerate to an airspeed very close to the stall speed. As density altitude increases, the effective stall speed of the wing increases, so to take off, the plane has to accelerate to a higher speed on the surface.
Any hull has, for lack of a better term, a "hull speed". The hull will accelerate to that speed fairly easily, but to accelerate beyond that speed something has to give.....you either have to apply huge amounts more thrust, or use some technique to reduce the amount of water drag on the floats.
And, if the floats hit their hull speed before the wing reaches its required flying speed......... You're a really expensive boat. That's what was happening with those early PeeKay floats on that 185. The later PeeKays are great floats, by the way.
The term hull speed really applies to displacement hulls, not planing hulls, as are used on floats, but the effect is similar, and it's very real.
To operate from the lakes you describe will require really superior seaplane performance. For years there was a Beaver operated from Tahoe. The Beaver is supercharged, so engine power remains at sea level, and the Beaver is a hell of a seaplane. That said, I understand they didn't operate on high DA days, and their loads were light. I doubt that plane would have launched there at max weight, but maybe.
Maybe the Zenith will do the trick. I think the only way you'll find out is to find someone with one and invite them to come demo. Might cost you some, but better to find out that way than to build one, then have to truck it home.
MTV