Yeah, that's what you are looking at my friend - your hitting the ceiling on that 20w power section. There are a couple areas where you can address this issue with limited to moderate success.
If you are wanting more volume, you will need to go into a better speaker (or pair of). The general consensus is that the stock Eminence designed speaker is the achilles heel. You need to find not only the correct impedance match, but wattage range. You need to find the most efficient speaker you can to maximize your rig. You might find that a pair of Greenbacks would do you right if you were willing to go into an external cab setup. While not the most efficient, they are low wattage woofs that sound damned tasty for the style you are going for.
Another thing you can do is to simply turn the gain and bass down. EL84s don't cope well with heavy bass and will shitee the sheets (in the vernacular) with too much gain/bass.
If you are feeling frisky, you can dig up the schematic of that amp and see where those 6BQ5s are sitting with respect to volts on the pins. Most designers run these hot, but some run them cold for longer life at the expense of headroom and tone.
For a bolt on solution that involves only a few wires, you can look at a slightly larger output transformer. Some of that flub might be from a saturated OT. You'd have to check the chassis to see if there's room for the iron. This solution is more speculative.
The easiest thing for you to adjust is your expectations haha. She's a lil' sweet amp. I loved my Boogie DC-3 head - and intentionally bought it in that format, as I liked the idea of using different cabs as needed. It wouldn't be too much work to transform that combo into a head - chances are you could slip that chassis into one of their head shells..
She would sound phenomenal through a 4x12, but there, too, you will see that you hit the ceiling really quickly. It's just a bit louder before you reach it.