what replaced your Aerial 7B speakers?

Yes. From your electrical panel box to your wall receptacles. If you can run a dedicated circuit so no other receptacles (wall outlets) or lights are on the same circuit/breaker to your system.

Your amp requires all the juice it can get to run to its full potential. If your amp does not get the full load it requires it will sound thin and not power your 7Bs well. The 7Bs are a demanding load and with a small amp or even a big amp not running correctly your system will sound lean with no bottom end or as some say the 7B can be too polite which it’s not; they are not giving the 7B the power it demands and sometimes it’s more than just having a big amp as I’ll explain next.

If your system is say 50ft feet from your panel you may not have heavy enough wiring in the wall, not unlikely you have 14 gauge where depending on the distance you should be at number 12 or even 10. Your system is drawing a lot amps than say a couple lights, a computer and etc. Your amp will work but it’s not performing ideally. It’s kind of the same idea of using a table saw with a small gauge extension cord that’s 100ft long. It will work but in time you will burn the motor up. That’s why they sale heavy gauge extension cords as well.

If you live in an apartment there’s probably nothing you can do but if you’re in a home it might be best to contact a electrician to see what your options are. Then next step is throw out the $2 spec grade receptacles and spend $45 or so for a Porter Port - Hubbell outlet or better. A lot of people will run two dedicated circuits to keep their digital away from the analog.

Most house electricians are going to think you’re nuts, so just ask if it can be done and what the cost is. If you show them the specs on your amp they may get it but don’t bet on it. I think you’ll get more bang for your dollar doing this than spending the money on a new set of speakers which I don’t think is where your problem is. As several other 7Bs users have noted, the 7B is cabable of very good low end.

Good luck and keep us posted as I know many users have the same problem and don’t really know it. If you think I’m crazy you could do an experiment which I’ve never tried but I bet it will work. Go to the closest outlet by your electrical panel and go to Home Depot and buy a Ridgid 10/3 extra heavy extension cord and only plug your amp into it. They sale 50 and 100ft cords so only buy what you need. Carefully unpack the cord because after your experiment you’re going to return the cord or keep it to cut up and make your own power cords for your equipment or for your table saw. Again I’ve not tried this but I wouldn’t be surprised if it works. Now if your system is right by your electrical panel a dedicated circuit will be easier but my experiment probably doesn’t make sense. It’s about dedicated circuits and what is the distance of the wiring and sizing it properly or you’re wasting your time and money. Don’t forget to buy decent outlets if you haven’t done so already.

Thanks for the explanation. Makes sense.

I have not done that of course. But, this is a 90 year old house that we renovated about 8 years ago.

Most of the wiring was original but was the old two prong type outlets. So when they added extra 3 prong outlets to the room they ran them from the panel and they do not share any lights etc. Just the new 3 prong outlets in this room. About 6. So I'm pretty close to a dedicated circuit.

When I'm listening the TV is off of course so the only thing plugged in and running in the room tends to be my laptop and a lamp or two.

So, not a dedicated circuit, but fairly close. Standard gauge wire and outlet of course.

I have owned the BAT and the bass can be a bit soft sounding.  I moved from Aerial 9s to LR5s (105 lb monitors) on 70 lb Sound Anchor stands and then added two, Aerial SW12 subs.  The combination of acoustic suspension (i.e., sealed box) speakers and the power and control of the SW12s have created as close to perfect bass as I have heard in my system.
Keep your 7Bs and add a pair of used SW12s on SA stands for your $4,500 and the sound will change your sonic world.

I honestly think there's more you don't like than just a bit more low-end. 
I don't want to put words in your mouth, but if you want a speaker with a 12 inch woofer or a facsimile thereof, fine. Get bigger speakers and hope they'll make you happy.  Take a long look at Egglestons, even used ones. 
They sound like music, have had nothing except very positive reviews by everyone, and go down to 19 Hz. If they don't do bass in your room, it's not the fault of your speakers. I had the Andra I and II, previously owned by the guy that sets up demo's all over the world for Wilson Audio ( a long story). He raved about them, also. Andre Previn (RIP) also had a pair. They have other models of course, a bit smaller, too. They are very well made, too- the grills are held on by invisible magnets. I can only recommend speakers I've owned. 

Egglestons are great speakers but they’re not going to offer anymore low end in a room that is 16ft deep than a pair of 7b’s. A 16’ deep room is going to go down to 35 Hz and that’s about it, which for most of us is fine because unless you’re listening to a pipe organ a full upright bass may hit 40 Hz. You could throw the largest Egglestons or whatever in there and it’s not going to change the physics of a 13’ x 16’ room. Also remember the OP is wanting to stay in around $4500. Maybe some room treatment or bass traps might be in order here.