Turned Off My Subwoofer ... And My Speakers Sound Great

Get a pair of small REL subs and hook them up to your stereo outputs per REL. Place them on diagonal corners. Fantastic SQ. This was recommended to me by Jacob at the REL helpline.

Actually, you don't have a problem. A problem is when you can't fix it, or have to fundamentally disrupt the experience. You very likely do not need new subs, or an array. You haven't even tried reconfiguring it yet, so the suggestions to move to another setup are a shot in the dark, quite out of line for first approaching the situation as described, imo. 

"By all objective measures..." which is why the audiophile should not depend solely upon measurements! They are a great guide, but you have to explore, experiment with your system. It seems like you just did an initial setup rather than push through trying all the permutations available to you.  

You are experiencing the normal situation when a sub is turned off. You are focusing on the mid-bass through top end, which is less noticeable when a sub is running. I review speakers and have them playing sans sub, then often add a couple subs. BTW, I do agree that if one is after superior results, the attempt should be to have a minimum of 2 subs. Having heard smallish sub arrays, I haven't been terribly impressed by them. I prefer to have two prodigious subs than four smallish ones that can't do the LF. If one had four larger subs, that might be a different story. But, then you might be into consideration of what that money might have gotten you in terms of a superior/upper end pair of speakers. YMMV 

Note: When  sub is turned off and suddenly everything seems so much better, that's a strong clue that you had the output of the sub way too high. Crank it back until it's barely discernible, then turn it down just a touch more until not individually discernible. Then see what you think of it all. 

Switch back and forth between sub/no sub. Enjoy it! Learn how the sub affects the sound, and I concur with others here that if things are THAT good without the sub, you likely had it set up wrong. Redo the sub settings with an oh, so gentle touch on the sub's output, and you likely will love what it does and not lose the benefit of the mains shining through. 

The only way I like my sub is at the lowest frequency crossover setting, and the gained turned down so that I rarely even know it’s on.  I also much prefer the high level input from the amp vs the line input from the pre.

If you can actually hear your sub or detect where the bass is coming from at it's location then it's either too loud or xover incorrect or likely both.
I have two subs.
I feel the bass but I stare right at one sub but cannot detect any bass coming out of it in my listening position.
I quite often forget there is two as second one I cannot see from my listening position.

@rib61 - TAS reviewed the JL Audio E110 sub that you have and talked about the software available for dialing it in. Something that be worth exploring....

https://www.theabsolutesound.com/articles/jl-audio-e-sub-e110-subwoofer/