Gregg, dunno how much playing the amp has, but the Fender blue alnico's by Eminence were noted for having a very long break in curve. Lets say that they're broken in though. So, to tighten up the bottom of a tube amp, you have to look at its circuit. At close 18 years old, the main capacitors are getting to the point where they might consider retirement. Tubes... if you can find some 7581's those are the 5881's on steroids, and deliver 35w each in the same envelope with the same heater spec. But, the real gotcha on the Bassman 5F6's is the way they have things arranged. What you've got is two gain stages, then a high current (relatively) cathode follower pushing the tone stack, then the driver. Those two gain stages cascaded is going to breakup. The FIRST preamp tube on the input side of the amp is supposed to be a 12AY7 for the original layout. But nearly everyone runs a 12AX7 there. I suggest you verify the 12AY7, trying a few types. The 12AT7 would also be worth trying, but they're not noted for being spectacular in the input position. For the SECOND tube, you want a very high headroom, chimey 12AX7... and you'll have to experiement there. BUT... you might find that double 12AY7's tames things a good deal. The circuit shouldn't really fart out too bad on the low end, but should be very rich in the mids, and breakup pretty evenly across the board from low to high. You might actually try playing bass through it for a bit to make sure the speakers are broken in. FWIW, the 10ALK (Fender Blue Alnico) is one of the better 10's out there once broken in. Fender realized this, but the consumer market wanted a speaker that sounded great out of the box - hence those speakers/amps got a bad reputation for brittleness and bad low end. All of this went away with some playing of bass through the amp, which loosened up the spiders and surrounds.
The best 10 guitar speaker for low end that I ever tried was the older Celestion Vintage 10. I have not tried the revised one, but the old ones kick major butt. Right now I've got a 2x10 Tremolux in a combo cabinet - 35w, tube rectifier, and it does not fart out on the low end, so the speakers are up to the task. I've also got a 2x10 blackface Bassman that moves huge amounts of air with the Vintage 10's. Folks comment on the breeze they can feel on their leg! I've played with that amp to break up nicely after about 4-1/2, but the low end does not fart.
I dunno.. hope some of that can help ya. One of the reasons I prefer the earlier Bassman, like the 5E6, is the older pre-Baxandall tone stack ensures thick mids, while the Baxandall type is mid scooped as used by Fender (and the rest). The thick mids, to me at least, are the essence of nice breakup without shrillness, or farty-ness. Starting with the 5F6 (1959) they used the more modern tone stack, but kept the two stages of gain prior to it... eventually moving the tone stack between the first and 2nd gain stage in someof the brown face, and all of the blackface series of amps.