PREAMP TUBES
Mesa simply rebrands with some extra QA/QC but has changed SPAX7's over the years, so it will be important to ID the tubes. Here's a rundown of OEM tube brands/models:
Chinese (good dynamics and overdrive, but hollow in the mids),
Sovtek WA's (harsh / biting)
JJECC83's (dull and dark).
Tungsol RI's 12AX7's have a lot of chime.
Sovtek LPS tubes are round and full.
Electro-Harmonix are bright.
NOS RCA long-greyplates ($20) work nice in V1 to give a lot of clean snap to the fender channel
NOS Raytheon long blackplates work have great everything, dynamics, smooth, mids, very tasty balanced tube.
Right now in my Heartbreaker I have: V1 RCA, V2 Raytheon, V3 Raytheon, V4 Groove tube gold Chinese, and Raytheon in the PI position (forget what tube position). The effects loop send/recovery tube I can't recall, but I would use the same tube as in the PI simply because your channel masters and master will respond more neutrally if both those tubes are the same. Alternatively, if you put a bright tube like the EH in the Effects driver position, you can use the channel master to dial in post-preamp brightness.
The reverb driver should be a 12AT7 to get the fullest reverb tone. There are only certain tubes that can stand up to the hurt in v4. Chinese, JJ's and NOS are the only ones. Most anything else will blow in 0.01 seconds.
POWER TUBES
Groove Tubes rebrands as well, and I can't find the OEM of the GT EL34. Mesa-branded EL34 (STR420's) are Electroharmonix which are bright EL34 tubes. Most other EL34's are darker than these.
If you are seriously looking at 6v6's, I'd recommend going through a tube vendor like thetubestore etc., and begin the path of really knowing what brand, model and spec your power tubes are. On page 8 of the Heartbreaker schematics available on webphix.schematic-heaven..etc...you will see the power tube voltage and bias parameters you have to work with, and you should give your vendor this info, as well as your intended switch settings so they can select a matched pair of tubes that will bias properly with these parameters. The three most popular new production 6v6 tubes are Tungsol RI's, JJ's, and TAD. Tungsols are more EL34-ish in their compression and breakup, but are smoother on the top but not as punchy in the mids. Overall, a tube that makes both sides of the amp sound pretty good. JJ's sound like mini-6L6's, but better - probably the best 6L6-ish tone I've heard to date, even though they are 6v6's. They will sound superb on the love channel, but not as good on the Lust channel. I'm about to order a set of Tungsol RI 5881's on a recommendation I received based on describing what I liked about the different tubes I've tried. BTW, despite Mesa's markings to the contrary, 6v6's bias like EL34's, not like 6L6's per the bias switch. And JJ's bias like 18W 6v6's not 12 or 14W's. I actually run 6v6's and EL34's in tandem when I gig...pretty great tone.
TONE CONTROLS: Wow, you are struggling with bright. I'd be reasonably happy with all my controls at noon, but my preferred arrangement is about G=10:30, T=1:30, M=2:30, B=1:30, P=1:00, CM=12:00-1:00, M=10:45. Both channels roughly the same.
You may have more luck on the Lust channel with the bright switch on, and the fat switch off. I run heavy mids on the Love channel because it cuts a lot better.
One further thing: the gain control has a 'bright cap' on it which is a very balanced value...my sweet spots are much lower in gain than what you are showing. My settings sound killer no matter whether hi (normal) or low gain settings are engaged. No substantial volume jumps either.
SPEAKERS: Don't know what the "stock" speakers are (heard they came in Vintage 30 and MC90 configs....I will assume they are MC90's). Also, if they are 8 ohms in parallel, that will give 4 ohms, or 16 ohm spkrs in parallel are 8 ohms, or 8 ohms in SERIES is 16ohms. I didn't like my MC90 with the Heartbreaker, but it may have sounded better broken in a lot more. They are dark speakers, with their large dust cap.
Basically, the MC90 has a strong high frequency rolloff to compensate for the "buzz saw" with Mesa's more conventional ultra high gain tones. If you are looking for classic low to mid gain tones, then you really really need to explore alternative speakers. Find or buy some Scumback M75's configured to get a 16 ohm speaker load. That will give you awesome cross over tones across the Love and Lust Channel. They are smooth on top, but don't get 'smooth' at the expense of brightness, like the MC90.
IMPEDANCE MATCHING
If you are using a single pair of EL34's (or 6v6's), you should be running a 16 ohm speaker load from the 4 ohm jack, or a quad of them from the 8 ohm. If you are using a single pair of 6L6's then a 16 ohm load from the 8 ohm jack. You can see from this that a 16 ohm speaker load is the most desirable to optimize tone and flexibility with all the tube combinations.
GUiTARS, STRINGS, CABLES, etc. Your guitars and pickups appear to be fine. I switched from D'addario to GHS boomers recently and find they deliver more balanced and less 'snotty' tones than the D's. May want to research web opinions on Monster Cables. I believe it has been said that Monster makes their ends a few thousandths bigger than spec which has the possibility of reaming out your input jack. There are mixed opinions on the tone coming from Monsters as well. Some hate, some love.
All of this post is my opinion.