Most of what you said was Greek to me.
But I barely speak my own language, English


OK, summary in layman's terms is in order. I'm not saying your a dummy. My only goal is to help you decide from what I know (or think) to be true.
Matching up the ohms is not critical, not harmful to your BX or the cabs, as long as the cabs would be able to handle the power if used individually, and you don't go nuts cranking it up.
You will get a little more power in watts if you run two 4 ohm cabs compared to one 4 and one 8 ohm cabs. Set the switch to 2 ohms for either.
Running a 4 ohm cab and an 8 ohm cab will result in the 4 ohm cab getting more power than the 8 ohm cab, but it will not be the ratio of 4:8 when actually playing music, i.e. your bass.
If you are looking for other than a Carvin 15, it would be good to get something that you can return, because it might not get you what you expect. I think the Carvin is more likely. If Carvin will sell you one rated at 4 ohms or you can find a used BR 15, I think that's your best bet.
My opinion on amp vs. cab power ratings, in this case, it would be best to get a 15" cab that can handle at least as much as the 2 x 10's you have now; 400 Watts RMS (aka continuous).
With the cabs you have now, or whatever you may move onto, use caution cranking up the bass knob, parametric eq with the frequency turned low, or the leftmost bands on the graphic eq, as well as the master.
I hope this is a bit more clear. Please let me know if any of it's confusing. I took quite a few medical and science classes, and I don't even come close to understanding that terminology! Latin is Greek on steroids!
You should also know the BX700 puts out 550 Watts if using a single 4 ohm cab, so you want to be double cautious if you use a single cab sometimes.