I know of no tube amp designer who uses SPICE. can you name a few?Nope. Maybe one? I know I don't! Victor Khomenko was trying to model our MA-1 in Spice many years ago before he became part of BAT. He called me up saying that the amp didn't run in Spice, but I had to point out to him that the amp actually worked despite what Spice came up with :)
As you can imagine, the ratings of the tubes tend to vary with load- and the amp will draw less power and run less heat if a higher impedance load is used. Also, as you've pointed out, the class of operation is affected. In our case the amp is biased to be class A2 on the proper load, but will be class AB2 if the load impedance gets low enough. We don't get crossover artifacts on that account though.
As far as high current spikes, at full power the tubes still have some dissipation left over, so they can handle spikes, however as the load impedance is reduced, eventually this will cause the cathode coating to fail.