The variable aperture doesn't bother me, since I have a modern camera that maintains the set f/stop when I zoom, except of course for the rare times I'm shooting wide open.
Me, too - I've got no problem with my var aperture zooms, esp. since the digital bodies remember what the min. aperture was and go back if I zoom back. When shooting in very low light it's a bit of a hassle to set my 70-300L to the longest f4.5 or f5.0 setting, but I'm even used to this since I have got these zoom types for a long time.
If you want a f4-5.6 zoom act as a fixed f lens, just set it to f5.6... actually, I don't understand why people have a problem at all with this, I don't see these zooms as loosing on the long end but gaining extra f-stops on the wide one. If e.g. the 24-70/2.8 wasn't fixed, maybe it would could be a 24-70/2.0-2.8 with the same iq?
I'm going to try out the 70-300L f/4-5.6 this weekend and see how I like it compared to the 70-200L mk2 f/2.8
As with all lenses, there's a compromise - the 70-300L hasn't got a fixed aperture (nor an internal zoom mechanism), but gains shorter build and due to not having f2.8 less weight and much smaller price tag, so I got it because for me the 70-200 is too short for a tele, the f2.8 dof is extremely thin and its a total overkill as a walkaround. But there are many good threads comparing these, and I'd exchange my 70-300L for a 70-200L anytime for free because of the better af @f2.8 :-)