Hi billyjoe,
I'll assume your use of the word *Gain* means some kind of OD/distortion?
That big fat rich OD is coming from the power stage not preamp triodes.
Triodes are only doing voltage amplification/ Voltage gain.
Generally they only do halfwave clip which aids the powerstage fatness a bit but without additional circuitry,,, No big fat distortion comes from them.
The whole point of tube amps is power stage compression without that you will be eternally frustrated.
You can build a no frills EL84 amp with 2x AX7 and 2x EL84 with all the gain you will ever
need,, just by refining the *POWER STAGE*.
Maximising the compression effect *Inside the powerstage* is the secret to success.
In the words of King TUT; "If you want MAX tubyness then simple cathode biased amps are for you." All the bigger stuff is much harder (READ $$$$) to get it to happen.
I personally went round in a big complex multi triode preamp circle and now I use one of the first tube amps I ever built.

a very simple cathode biased amp. (2 knobs,, volume and tone.)
ALL the rest is done via external mostly SS little trick circuits I've built.
When I do need extra volume I just take a speaker line out to a second 120watt SS poweramp and a big quad box.
This negates all the needless complexity and expense of big tube amps.
I play at a local muso club and I'm competing with Cyber twins, Carvin legacy's and the
manditory Fender devilles. I have no problems pulling all the needed tones of a good guitar rig. If truth where known I think it pains them moreso because they know I'm also using a $150 stock chinese strat copy.

The master volume era was created so one could overdrive the input and adjust the master to lower level. Although it may seem like a logical step it's conterproductive as it kills off the magic of the power stage. That's why you don't split valve preamps from valve power stages with things like efx loops or SS reverb loops as you break the magic bond between the preamp and poweramp. SS amps are completely different so fine do what ever you want but tube amps work best as one complete unit.
My learning is thus; **Little amps always sound sweeter**,
because by design the amp spends more time in *Powertube Compression* mode.
in a nut shell;
The bigger and stronger the power stage the harder it gets to make magic as the bigger amps have to run a lot louder before they compress and the power supply sags.
You fight an endless circle constantly adjusting between preamp dist and master volume.
some big fenders run so clean you may as well be using SS.
Re heaters;
Don't worry bout that for now as you are obviously considering gutting this amp and if you start out with a simple EL84 powerd Ceriatone kit you won't ever have to concern yourself with needless complexity of DC heaters.
Re gutting the amp.
The trinity hiwatt uses 6v6 or kt66 so not even close, different tubes give different
sound/tone/feel/dynamics. but hey if it's well thought out it might be just the ticket.
Get this one nailed on your list of things worth knowing It may help unravell some
confusion when discussing power valves.
TC (transconductance) in simple terms *Gain*
(the most over used word in the amplifier world)
TC of common guitar power tubes,
(Tetrodes verses Pentodes)
T 6V6 TC= 3,800
T 6L6 TC= 8,000
P EL84 TC= 11,000 (apprx)
P EL34 TC= 11,200
Armed only with that info even a novice can now see why the term,
"British sound verses American sound" comes from.
The Type of output tube makes a big difference to the end result.
An EL84 only needs a 30 volt swing on it's grid to go full output whereas a 6V6 needs about 70 volts swing. (I think a KT88 needs 90 odd volts on the grid)
Now that does not mean that a 6V6 can't produce good distortion but you have to know how to build an output stage and know the tubes you are using.
The Tone stack in the SA412 it the best you'll get and you can build it as a stand alone unit if you wish and take it with you to any amp.
Read my blab under Schematics and layouts
http://www.ssguitar.com/index.php?topic=1136.0Keep in mind a big part of Hiwatt sound is due to the use of *FANE* Speakers
Some homework;
Try Valve wizard pages,, Tone Lizard site (go to the tone lounge for some good grounding in Valve gear.
Have fun Phil.