Making a class G or H or whatever system just sounds like inviting disaster, or at least making more trouble than it's worth. You get much higher, and much more variable, Ccb at low Vce, so your loop has to be slower to compensate for it anyway.
Face it, you're making a 1kW amplifier. It's going to get hot. It's going to be big. It has to be big! No, it literally must be big: to get low inductance, you need many transmission lines connected in parallel, or very wide ones.
I don't know of anyone who makes coax that'll be nearly low enough impedance to be worthwhile. You'll burn your inductance spec with just a few inches of 50 ohm stuff.
Purchase a box of two-sided copper clad. A hunk of that makes a parallel-plate transmission line with an impedance of a few ohms. Stack all your transistors along one edge, and connect the load to the other!
Regarding device choice: BJTs have more gain period, and you need all the gain you can get. You do need high current AND fast devices, but common audio parts will suffice -- they often have fT peaking over 60MHz.
Looks like D44VH10/D45VH10, 2SC5001/2SA1834 (caution, low voltage), 2SC6017/2SA2169 and PHPT60410NY/PHPT60410PY are reasonable candidates. The SMT ones you'll obviously need more of, unless you're okay with pulsed operation -- which is an interesting way to go, and should be good enough for something like this, really.
Otherwise, using more devices means potential bandwidth savings, as you could use lower current, higher fT devices maybe.
A classic audio part would be Sanken 2SC2921/2SA1215. A few bucks, but made to dissipate power, and run in a linear amp. Not as fast as the others.
Offhand, RF transistors that are suitable would be,
MRF1150MB, MRF454, MRF455, MRF429
They're >=10A each, and >$30 each. You'd need a few dozen, so it's not a cheap idea, but it would be more than fast enough. Keeping them stable, and supplying fast enough drive, would probably be... interesting. But hey, I'd accept the challenge!
Tim