Just echoing what others have already said by now, but...
I made a similar trip over there about this time last year (late February), also in a 180hp Archer. No problems with the aircraft performance, particularly as the weather was quite bad and the temperature not too high - (low 60's in Phoenix, low 40's at GCN - there was snow on the ground). We actually got stuck in Las Vegas for a day due to seriously crappity weather and had to cancel the planned trip out west to Death Valley due to snow storms over the mountains. Even if the weather had been hotter, performance wasn't an issue as of the places I went - even the smallest of 'unmanned' airports had around 4000ft of tarmac - long by my standards.
Departure from KGCN was the most challenging we had, performance wise. It's a very long runway, but the climbout is over trees in all directions with no clear place to make a forced landing. At perhaps 400ft per minute (2-up), I was quite a distance from the field before I felt truly comfortable. The FBO at GCN is adequate, but nothing more, with no real facilities or even room to do proper flight planning. Fuel was understandably expensive too.
I wouldn't worry too much about the VFR corridors over the Canyon - so long as you've studied the chart, the landmarks are quite easy to spot - there are disinctively shaped ground features all over the place. When we were there, I made regular position reports but we didn't see or hear a single other aircraft (midweek, about lunch time if that makes a difference). 10,500ft (southbound) was no problem in the Archer - and after we cleared the special airspace I actually climbed up to about 12,000ft - just for the hell of it - and she still wanted to go higher.
If you're going to Vegas and want to avoid the high parking and fuel charges at McCarran, North Las Vegas (KVGT) provided excellent service including a free shuttle to downtown hotels (but not return). The 'Showboat' VFR transition takes you in from Hoover Dam, just south of McCarran before turning right into KVGT. If you do this, the controllers are very helpful, but BE CAREFUL with your assigned altitude - I was 'told off' for exceeeding altitude by about 70 feet - and there was an Embrear 140 passing about 200 or 300ft above us, so I can understand why. We deprted VGT to the north east under the control of Nellis Approach - they were very helpful and vectored us around their area as there was quite a bit of military traffic.
Whatever you choose to do - enjoy it (it'd be difficult not to) - and let us know how it goes - I'm happy to talk about this stuff all day (as you probably guessed by now), so PM my if you like.
Oh, and thanks again to David Viewing whos website was really useful in planning my trip - I'd just about decided I wasn't up to the Canyon overflight before I read his advice.