Can you even get reostats in those values and powers?
Don't put the reostat between rect and first cap. Yes, the RMS heating is much more than just the DC, and the difference is a nasty computation.
Don't use reostats. Get a 10-pack of 1K 5W resistors and use as many as needed.
Doesn't have to be 300.00V. The amp will work at 270V or 330V, with mild differences in headroom.
That heater supply. You are doubling-up to 18V but using 6V. Total DC load is 18V 2A or 36 Watts. Winding is rated 6V 5A or 30 Watts. There's no free lunch. The winding is 20% over-loaded.
Also the 18V-6V or 12V drop in dropping resistors will be less if a tube is pulled for diagnosis; perhaps putting 9V on the remaining tube(s). That's not quickly fatal but is rude to the tube.
Agree that 6.3V AC never gives a happy 6V DC.
Can you wire your heaters series 12V? Then you need 12.6V at 0.9V, which is easily had from 6V 5A doubled.
And a series-string with one tube pulled goes dead, not un-sag to a higher voltage. (Anyway you won't need 2/3rd sag, maybe only 20%, less up-side risk.)
_I'd_ go the whole way. Lose the hollow-state rectyfire. Strap 6V and 5V windings for 11VAC, doubles to 29VDC, can feed a 24V string. (Ah, 3 bottles per unit, a 19VDC 0.3A goal seems best.)
And higher-volt series-string allows you to put the sensitive cathodes "elevated heater" as Ian suggests, though note that in the Cimema several cathodes are already up at 8V so "elevation" does not happen until 10V-12V up the string (put the push-pull stage at the groundy end).
Again, I'd get a 10-pack of 1r-10r 5W/10W resistors and use as many as needed.
The diodes should be rated for the _winding_, with a generous margin. 5A winding needs 5A diodes at least. The added cost of 10A parts is less than the added cost of replacing 5A diodes at an unsuspected moment. (And I'd use 400V diodes because line spikes do happen and plain Silicon isn't more expensive in DIY economics.)
Capacitors should be >1000uFd/Amp, much greater with today's low-cost low-volt caps. Assuming 29V 0.3A, >300uFd. The first doubler caps could be 2,200uFd 25V, the next two may as well be 4,700u 35V.
Ripple is then 0.2V at first caps, about 50:1 reduction of 100/120Hz in each RC, 0.1mV ripple on the heater line. Don't wrap it around first grid; otherwise this is plenty clean.