I have compared the EL34 and STR445 in the BAD side by side as I have two BAD 100. Those almost sound the same but need to puss the channel volume up with the 6L6 tube to be at the same level as the EL34. STR440 was a bit thin sounding. STR445 was aggressive as were the STR448 (grey color, tried the reds and it was lame). Consider the BAD is a Class AB so it does rely on power tube distortion to some extent, probably more than you think. The same goes for any Mark amp too. The early dual Recs and including the Roadster, that was more preamp than power tube distortion. I would exclude the MWDR as that amp can run with the STR440 grey and not sound like mud (that is what the Roadster did if I ran green or grey color codes). As for the STR445 in those amps, not a fan. However it sounded really good in the BAD. Almost liked them better than the EL34 until I compared the two amps. STR448 in grey were also great, similar to the STR445 but with less of a 6CA7 character as the 445 tube. No rule of thumb here. roll with what you feel sounds best.
STR440, meager sound. Not sure on the STR430, if they sound like the STR443 it would not be far off of the STR440. Actually you do not get that pissed off bees sound with the 440 tube in the BAD like you get with the MWDR or Roadster. Odd how things sound different with amps that have different OT. Have to say, I am after the more aggressive grind but still admire the clean channel, and any note detail and definition you can get even with moderate gain levels. Probably why I like the BAD so much. It is on par with the JP2C in many ways and it seems to be on the same page as the Mark VII, still different but yet enjoyable.
Trying to get past the dc coupled cathode follower tone stack driver on the clean is difficult. I doubt much can be achieved in getting that Fender clean sound. It could be the characteristic of the JJ ECC83S (Mesa's stock 12AX7). An old Mesa Chinese tube from the 1990's may change things on V2. I have also run a JAN/GE 12AX7WA in the cathode follower positions on the Roadster, that had some good results to brighten things up a bit. Never explored to the preamp on the BAD to see what works and what does not. I like the way it sounds as its and had no need to do any trial and error things on an amp with valid warranty.