> the 12AX7 ...has a plate dissipation of about 1watt. That would seem a decent pushhhhh.....
It takes a heck of a lot of voltage to force 1 Watt through a 12AX7. Mostly they run about 0.060 Watts, like this one.
> ie input tranny, 2 triode stages
In the Ampex 351:
input iron: 23dB, 1:14
1st tube: 21.5dB, 1:12
2nd tube: 22dB, 1:12 into 250K
estimated -6dB into 10K load
total gain before rec/play switch: 66.5dB, 1:2,000 into 250K
estimated total gain before rec/play 38.5dB into 10K load
line output stage: 25.5dB, 1:19
total available gain: 92dB, 1:40,000
So there is a lot of voltage gain after two triode stages, but only for high (250K) load. 38dB into 10K is not a lot of gain.
Also the 12AX7 is running only about 0.5mA. If you have inputs like Peter's, they need 0.25 to 0.5mA peak (3VRMS in 10K-16K). You can get almost 0.5mA peaks from a 0.5mA amplifier, but it will be grossly distorted.
At a minimum, I think you want a cathode follower to present >250K to the 2nd stage, and flowing 2mA or more to give solid drive to a 10K load. With 12AX7, that probably means 200 Volts across the tube. You might be looking at 12AU7 or other fatter tube. Overall gain is 66dB.
You will always (in audio) get more power gain with plate-loading. The existing 12AX7 is unsuitable: you can't wind a good transformer for a 60K source. And if you could wind 250K:10K, that is a 5:1 or 14dB loss of voltage gain, just 52dB overall gain. What you do is follow the 2nd stage with a low/medium-Mu tube like 12AU7. Even then, the plate resistance (about 6K) is high for a transformer. For good triode loading we want over 10K primary. The sound card may have radio supression caps that expect less than 1K source. 10K:1K is 3:1 voltage. The 12AU7 will give nearly full gain, say 18. The tranny gives 3:1. Overall gain is 1:6 or 15dB. Input impedance is high, so with the first two stages we get about 66+15= 81dB gain. A naked 12AU7 with transformer working at line level is not dead-clean like the 12AX7 working at lower levels: that's why Ampex went to a 2-stage push-pull line amp, so they could get some feedback. (And so they could drive true 600Ω loads.)
There is more gain in the 351 electronics. The first two stages are heavily socked with local feedback. Ampex was not building a Fender. You could throw some caps in there and get another 10dB-12dB gain. But now it isn't an Ampex 351. Do you want cheap or do you want good? Tube amps always want one more stage than you budgeted for. (No matter how big your budget started.... look at the McIntoshes and the Audio Research amps.)