I am very familiar with the Eden XLT-210, used to own one. It was loud as hell at low G and dropped off like a rock down to low E, which drove me nuts.
And I have learned to hear the difference between low-mids and true fundamentals in 40-80Hz range. (For years I played gear that had effectively no response down there, so this is relatively new to me, like last 10 years or so.)
I wasn't slamming your EA cab or your hearing, just speaking about bass cab design and use in general. I've heard nothing but good things about EA but have only played a 2x8 cab, IIRC, from them years ago that I found very impressive, like an original SWR Baby Blue combo. That cabinet didn't have much in the way of extreme lows but was very tight and even across the range it did cover and a great onstage bass cabinet for PA's with subs to handle the bottom for players using the PA for bass. I generally don't, but I have engineered for shows with players who did and the PA handled the bottom while the smaller cabinet provided stage volume that worked well with it. Your own experience with what was once considered the industry standard of bass cabs, the Eden XLT, demonstrates that you had to train your ear to what your bass cabs were actually doing and once you did, it was eye opening. Most bass players don't and other cabinets are designed for volume or attention rather than even tone.
We had a Schroeder 1210 and an old Hartke 115 and an Acme B-1 and I forget what else lying around. The Acme was very smooth too, the others were all over the place, each in its own way.
I have an Acme Series 1 4x10 and it is my benchmark for good tight, lows and it has both a midrange driver and tweeter, which I do attenuate using the selectors on the back. Most of my cabinets have a very similar inherent tonality to it, especially old SVT coffin cabinets, which are just as deep in reach, not as efficient in the bottom, but louder overall. Every post-1986 SVT is a different story, very little deep bottom at all. Ironically, my least low-end friendly cabs all are based around 15" drivers, which most people associate with low end: my Traynor YBA-1A 2x15 and Marshall JCM800 4x15, but the 2x12's I have, including my Bag End subs used as instrument cabs without the processor, have a great low end. I don't really care for "modern" bass tone since my attack is very hard and midrange-heavy already. I unhooked the horn in my Nemesis 8x10 because it made a great sounding bottom horrible in the upper mids and without it, the cabinet is plenty present already. I know when it was made, it was supposed to be a "budget" alternative to then-current 8x10's, including its upmarket brother the Eden XLT 810 and Ampeg's big ported 8x10's (discontinued when Loud bought them) and SVT 8x10's, but it has a better low end and smoother response than all of them. A perfect example of what I meant by true bass response making a 12" driver less responsive are my Ernie Ball 2x12's which have a midrange driver as a well as a horn and unlike most similarly equipped cabinets, the midrange driver and horn are not there to make the cabinet "extra present;" they just even out the mids leaving the 12's to focus on low end.
As to the EA CXL112L tweeter... I'm not sure if it's the horn (unusually large for a bass cab), the driver, the crossover, the transition between the horn and the 12, or all of the above; but what I hear is the upper mids are rather forward to the point of being a bit obnoxious. If it weren't for that, I could happily listen to CDs through it, or use it as a PA cab. I've certainly heard a lot of worse PA cabs. For bass, I usually turn the tweeter pad most of the way down.
It sounds like you like the same tone I do. Electro Voice's old SX series of molded 1x12 PA cabs, including the powered 1x12 subwoofer make nice bass practice cabinets and seem to have been designed around a similar philosophy, one that has been disregarded with more modern PA designs, most of which are powered, which favor overall volume and electronic tonal adjustment rather than even response. If you ever get a chance to compare one of the regular SX200 or SX300 PA cabs to your EA CX112L, I'll bet that they are similar sounding with your EA having a better bottom and more forward midrange. Before my health went, I was designing an 8x12 based on the SVT coffin but having more volume and bottom.