"...my usual setup with distortion" and "a fuller, more balanced tone" stick out to me. I assume the former involves some sort of pedal(s), since the identical channels of your amp have no gain control -- just volume and a three band EQ.
As for a full, balanced tone, are you able to get that, clean, through the Ashdown 410?
In my limited experience playing with distortion, I've found that being able to blend a clean, low-passed signal in with the distorted signal (whether full-range or high-passed) to be more useful in achieving a full, balanced sound than blending both signals together full-range (which tends to make the distorted signal sound wimpy - or did for me).
The pedals I've tried that do this are the
Amptweaker Bass Tight Fuzz, which blends clean lows with a full-range fuzz tone, and the
EHX Deluxe Bass Big Muff Pi, which lets you adjust the high and low crossover points, including overlapping them or leaving a gap in between the low and high bands. This was through a single cab, though. (There are also some dirt pedals that do a better job of preserving a full, impactful low end than others, even without fancy crossover or blend controls.)
If you're going to mix different cabs, I'd avoid running signals that overlap too much through them -- at least in the lows and low mids. You could use some sort of crossover or crossover-containing pedal for this or use the separate EQs on each channel of your amp as a crossover of sorts (perhaps EQ-ing out all of the lows on the distorted channel, for instance -- again, I've done this with a dual-channel preamp, but into a single cab or identical cabs getting the same signal).
There are a million different distorted bass sounds -- I don't know what you're going for and it's not my area of expertise -- but if I were trying something with your amp and two cabs taking different signals, I'd tend to keep the bigger one for clean lows (which will take more power) and the smaller one for distorted mids and highs. You can tweak the balance and EQ between the channels endlessly, but it's somewhere to start.
You could even use an adjustable HPF pedal (like an fDeck HPF3) to high-pass the distorted signal at something like 100 Hz and feed that (if you're very careful with the power) into a guitar cab or a simple 1x10 or 1x12 bass cab without tweeter. (Actually, if you like the tone of the
Bass Big Muff Pi Bass Deluxe, it has separate outputs that should allow you to run the dry signal into one side of your amp and the high-passed Fuzz tone into the other. You might also find an adjustable crossover pedal that will let you do the same (though, again, you can approximate this with a splitter and the separate EQs on each side of the amp).
Can't say how well any of this will work or recommend specific cabs or a specific splitter, but you asked for input and those are my thoughts, just spitballin'.
The other thought that comes to mind is that you've a Barefaced Six10 listed in your sig -- do you still have that cab? I imagine it would be more full and formidable than the Ashdown 410. You might that the right approach to pedals/EQ gets you results you like out of one cab, whether the BF or the Ashdown. Then again, it would be neat to try a distorted (and effectively high-passed) guitar cab or small combo for dirty highs.
That's all I've got -- I leave it to those who know more than I do about this stuff to comment further.
