Wow a couple things right off the bat.
Just because his "guitards" are running a 4x12 each it does not follow that he cant possibly keep up with only a 15" and a 2x10. I play with a band that has THREE guitar amps that all are all tube amps on 4x12 cabs. I get the job done with a 2x12 and a 1x15. I could be louder sure, but you will notice the second I stop playing. I am definetly in there.
As far as cutting through with mids. Sure mids take less power to generate than lows, but once you depend on mids to carry your tone you are on thin ice. That is snare drum, vocals and guitar amp territory. If I am in a battle for EQ real estate I retreat to the lows and the highs. It is usually easy to go under the guitars. The lowest they get is 70hz on a good day. Then crank in some 4k or so for that metallic clank.
But while we are on the subject of mids, the other day at practice all night long my amp was sounding weak and undefined. I kept playing with my bass' eq to try and make it better but it only got worse. I could hear bass, but no note definition. turns out my mid knob was on zero, fully cut. Must have brushed it with my sleeve? I brought it back up to 4 and it was all good again.
Ampegs. The solid state heads arent so great compared to the real SVT's but they do get loud. their cabinets are pretty lame IMHO. They dont go terribly low and they dont have much bite in the mids though having a mostly boogie rig I guess I am spoiled!

While their 8x10's are well known to be thunderous, the 4x10's seem to be very weak.
I know it may go against your taste about having an all Ampeg rig (and it does look nice when your amp and cab have the same brand logo/colors) I would check out Eden, Boogie, Avatar and GK. The GK 4x12 neo and 2x12 neo cabs are nice and light as well as sounding good and loud. Heck the 2x12 is 4 ohms, weighs 35 lbs and takes 600 watts!
two of those would handle 1200 watts. Take that guitards!
In the meantime I would try and focus on the eq. Figure out what part of the upper mid/treble you can use to define your notes with while boosting the bass your guitars cant touch. You can go for a midrangey tone also, and I tend to like that myself sometimes, but it only takes a new fuzz pedal on the guitars to wipe out that tone.
PS listening to the band you said you like, that bassists tone seem to be all low end and low mid with a tiny bit of treble. Could be the recording. Producers love to push the bass out of the way to make the guitars sound bigger.
But thats pretty much 8x10 territory. Lots and lots of low mid. OTOH 2x15 rig will go a bit lower and have a nice midrange clank to it.
Pretty much all the hardcore bands I have ever been in, seen or done sound for use 8x10 or 2x15. There are exceptions of course, but for mosh pit/slam dancing music you need to go low with authority.