In an ongoing effort to improve I feel that we've addressed these issues with the new generation. My current gigging cab is the new 66. The reason we went with the multiple 3's was to get an overlap in the mids/upper mids to do exactly what you say. A bit of a challenge crossover-wise. (glad we have Duke on the team).
Might not be apparent from my nitpickiness and the way I write, but the emphasis in my experience with the 2nd gen. 66 is on the "capable and versatile" part, not on all the things I'd change if I could have my ideal cab (whatever that might be) spring forth fully formed like Venus from the head of Zeus. Every time I've taken it out, I've gotten a better result with it, and the last time (outdoors) was very good indeed.
The hot/sizzly was my attempt to see how far to push the tweets to get a bit more high--high definition. Oops! Too far.
At home, for me, it's a bit much, but then I'm coming from a tweeterless (2x12+mid) cab. On stage, standing near the cab, it's less pronounced but still there (the overall effect is smooth, though). Out in the audience, even 8 or 10 feet, a non-issue, even for me. I think at some point I'll get it padded back a couple of dB like we discussed, but I don't want people to get the wrong idea. I've let a couple of accomplished players play through this cab while I listened and vice-versa. The only one with any nit to pick about the top-end was me, and that only when I'm on top of the cab. With any distance and a little volume, it's well integrated with the rest of the sound.
It's been mentioned that the cabs change character with volume, and that the effect begins pretty low. Not sure exactly where that begins or how it "ramps up", but I will say that I think this cab really comes into its own on the gig. I don't know where its limits are yet, as it's never shown any strain, but I'm enjoying finding out what it can do and how it behaves under different circumstances.
Miscellaneous note: Having gotten used to taking a little Markbass combo most places, this cab felt like a chunker to me at first. A couple of carries now and I'm used to it. It is still a two-hand carry for me (I can pick it up with one hand, but wouldn't want to go any distance that way), but an easy load-in/out. The kind I wouldn't have blinked at back when I still got any exercise! I even walked a block with it held to my chest -- don't want to do a lot of those, but it happened!