Nobody can do much for you other than guess. But as one who took apart many hundreds of old tube TVs in his wayward youth, I *can* say that I *never* saw a TV use a 5Y3. Not even one. 5U4 only...sometimes two of them, but for the most part, one. So if you are using a 5Y3 or 5AR4/GZ34 in your amp (2 amp heaters vs 3 amp 5U4 heater) then that's a biggish factor in your favor. Secondly, transformer-operated (vs series-filament) TV sets usually had a heck of a lot more tubes than say a Super reverb, and many of them might have been octals vs 9-pin, which implies more filament current, in general. If you go back and look at TV set ads from the late 50's, many of them boast "17 tubes!!". Lots of those tubes were 6SN7s, for example, using 600 ma heater, vs 12AX7 which is 300 ma run from 6.3 volts. OK, more modern, smaller tubes? Many of those pentodes were 7-pin 6CB6 = 300 ma, same as a 12AX7, so that's a wash. And you're using lots fewer of them. No damper diode tube which is another fat 2-3 amp heater. I believe a late 50's TV required maybe an 8-10 amp heater winding. Super reverb = 2 x 6L6 @ .9 amps & 6 x 12A_7 @ .3 amps. Little under 4 amps.
So as far as total heater current, I believe you would be way, way under spec for your PT.
That leaves output tube current. What's the conceivable delta? Grossly speaking, maybe 25 more ma than 6V6 at 500 volts? But then you've deleted all the plate currents for perhaps ten tubes and at 2 ma each, very light, that's 20 ma you're not using. No fat vertical oscillator, no big switching horiz oscillator, and those oscs weren't any kind of 2 ma tube circuits.
Frankly, I don't think you have a thing to worry about.