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Contact the manufacturer. In some amps this would be a VERY bad idea. Best case you would absolutely have to rebias. Worst case, you can destroy your power transformer, the tubes, and possibly other internal components.
Well ,if possible ,a more efficient speaker is the simplest way. Going from a 97db rated to a 100db rated speaker is like doubling the power of the amp! There is a very noticable difference in volume in my Chubster going from a G12-65(97 db) to a G12H-30(100db) Generally speaking with Celestions the medium magnet is 3 db less efficient the the large magnet models.
Of coarse this is moot if the amp already has an efficient speaker in it.
Definitely look into higher efficiency speakers first.
Even if the Badcat could use 6L6s, you would have to expect a noticeable difference in sound as they have very different(something like half) primary impedance specs compared to 6V6s unless you adjusted the speaker load to suit better.
Add to this the fact that Matchless usually runs their outputs at a mismatch to begin with, and you have a lot of variables that could easily just get you a sound that you don't like, or worst case scenario, some fried amp parts.
6L6s draw more current than 6V6s, and they produce more output. Unless the Transformers are considerably overbuilt you could have problems with both transformers due to that. Also, if the OT is designed to saturate slightly with the 6V6s for "harmonic complexity" it might sound nasty with even more power through it.