Ok, this thread has been beat to death and I haven't read all the way to the end. But I just wanted to hit on some of the more salient points.
A sub driver in the avatar cab may see marginal gains, but will probably still get blown by the op overworking it.
A sub driver in a new custom cab would fare much better but likely still fall short of what it sounds like the OP wants. Combined with bumping up the xo frequency (to say 150, but experiment), and probably bringing down the overall LF volume on the amp, it might be enough to get him there (but would be an expensive experiment if it failed).
A 15" sub driver in a custom cab optimized for low frequencies is the best bet for getting the amount of low frequency volume the op needs to match the 4x8. In terms of area, a 4x8 is a little bit more than a 15, and almost twice a 12 (let's not get into the esoteric and arcane arguments about cone depth and all that nonsense which lets be honest, doesn't make much difference in typical real world application we're dealing with). So to match it with a 12, you need an extremely high excursion 12 to make up the difference, vs an average 15. And the bonus is the 15 will almost certainly have a lower fs (what you want in a sub) and higher power handling (by probably 100w or more) than an equivalent 12. My guess is you could get a 15 sub cab that weighed in at 50 pounds or less. The downside is it would be completely worthless without the other cab, and is still going to cost a good chunk of change, and you still won't have a small gig solution (just 100+ pounds of big club stomping power). Plus the sub cab will have limited resale value since it's such a niche piece (more likely to find someone who wants to use it as a PA sub than with bass).
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Before I continue, what happened to the 4 kappas and the most recent blown driver? Did you trash them like an idiot, sell them as blown, or do you still have them? If you still have them, they could be reconed and repurposed in new cabs. Or you could sell them to fund whatever you end up going with. 2 2x12 3 way cabs could be commissioned for probably a reasonable price and I bet they could in in the sub 60 pound range, sound pretty good, and certainly be plenty loud.
But if you didn't want to do that, I would sell those old drivers for someone else to recone and use, and then probably commission 2 3 way "super 12" cabs. 1 should have enough low end for small gigs, and 2 should get you by for bigger ones. If you still somehow needed more grunt, you could run those 2 cabs with the 4x8, but I doubt that would be necessary.
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As far as the driver size debate, come on guys, are we still arguing about this? Driver size is not the be all/end all of parameters, and you can engineer a lot into a small or bigger driver. But size OBVIOUSLY and CLEARLY makes a difference if not compensated for with a LOT of design work. a 15 compared to a 12 compared to a 10 compared to an 8, etc... is going to have higher sensitivity, lower Fs, higher xmax, etc... It's not a rule, it's just a trend. As in, if you average all those parameters for each size class, those things hold true. Don't take my word for it, go look at a bunch of driver specs yourself.
And then just think about it with some common sense. How much xmax can you design into a 5" driver? Because that's how you make up for the tiny surface area so your displacement measures up and you can get some low end going. 15mm? 25? For a single 5 ti match an average 15, it would need to have a 55mm xmax. That's about the radius of the cone. Just think of how fast it would have to be moving to travel 55mm and how much power and control that would take. But you probably have some tiny 1-1.5" vc which can handle like 50-100w max.
So in the end, whatever you can engineer an 8 or a 10 to do (aside from high frequencies), you can design a 12 or a 15 to do better and more so. Because you're not trying to fight physics as hard. Sure, anything from 8s to 18s is "feasible" for bass in reasonable numbers (sorry, 16 5s that cost 2500 bucks and do almost what 2 15s for 500 bucks would do is not really "feasible"). But certain things are just way way way easier with the appropriately sized driver. On the other hand, there are some things that happen with a bunch of drivers that you don't get with 1 or 2. It just depends on what your design goals are, but for low end, when budget is a factor, it's hard to go wrong by going bigger.