You'll have a hard time finding BJTs anymore, that handle that kind of voltage and bandwidth. Even salvaged CRT drivers (typically fT ~ 1GHz, Vceo ~ 100V) won't cut it -- you probably need 150-200V drive here. 2SC3503 is basically the only holdout, and while it is fast, it's not quite that fast.
Driving it wideband, also dictates quite a low impedance: a typical sweep tube might have 30pF input, so needs a grid-line impedance of 106 ohms or so. You can get a little peaking from a resistive source into a capacitive load (30% or so), but not a crazy amount, even with a high order peaking network.
Example: I built this back in, uh, 2015ish was it?:
It's a proper 4-stage distributed amplifier. I'd have to look at it to see what the grid line impedance was, but the terminator I think is 4 x 470Ω in parallel, so close to 120Ω. I got about 30MHz out of it:
(input return loss measurement; never was able to get that final HF pole in line with the rest, which would've brought in a couple more MHz BTW, but adjusting these things is a PITA)
Bandwidth would've been higher if I went for a lower maximum power output; I used a singly-terminated plate line, which halves the bandwidth and doubles power (since it's not dumping backwards power into a termination resistor). Pushing into the 60MHz range instead, it would've been even harder to tune, or maintain stability even, due to electrode inductances being a real problem up there. And keep in mind, sweeps do not have particularly low reverse transfer capacitance; the screen grid, and electrode-connection area, make poor shields. You'll be much better off using RF types like 6146 (preferably -B), but you'll pay for them, too.
Or radial-beam or even planar types, but besides being rare, they're harder to use (special sockets, forced air or more).
It's much less interesting, but far more practical, to simply go out and buy a MRF-whatever power transistor and be done with it; even plain silicon types have bandwidth beyond a GHz, and low enough Crss or s12 to make use of it too. The circuit is simple, just a pair of bias tees, one rated for enough current to supply the drain, the other biased preferably with temperature compensation for stable biasing. Impedances are low (few to tens Ω) so you do need to design the matching transformers a bit carefully, but that's standard TLT work. Or use higher voltage types like MRF300 family for example, at the expense of lower bandwidth in part due to the cheap but poor choice of package, but capable of direct drive into 50Ω lines at reasonable power levels.
I also tried a pulsed test, in case sweeps or even those bizarro pulse regulator types perform any better at extreme cathode currents (which, in analogy with radar "hard modulator" types, should be permissible at modest expense to operating life):
https://www.eevblog.com/forum/projects/how-fast-are-tubes-for-switching/msg4676896/#msg4676896as you can see, the impedances are still pretty high, grid current now extracts a serious toll on cathode current ("hFE" quickly drops from a cool ~infinity for Vgk < 0, to low 10s for modest forward bias, to single digits for strong forward bias), and if you're trying to get high power out of the thing, you need to boost Va a lot, further costing impedance and thus bandwidth.
SiC MOSFETs are probably the best current option for pulsed operation in this regime, i.e. 10s of kW and ~ns; you could make a quite reasonable EFT generator, for example, using a small handful of them.
Tim