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

OP is very fortunate.
Wish my wife would dust around my listening room.

My wife is too scared to dust around the system 5000 volts and all. Mostly I just think she is afraid she would hurt something.

I think we need to think in terms of subwoofer system. I have never heard a system where one subwoofer did well especially with multi way dynamic loudspeakers. The advantages are not as great as they are for a one way ESL. 
Why system? The cross over is just as important as the subwoofers themselves and what comes with most subs is not even second rate.
If you are going to do this don't even bother until you are ready to buy at least two subs and an out board crossover that includes a high pass filter for the satellites. To get a subwoofer system right on you need a selection of cross over points and slopes, high pass and low pass need to be independent. Then you have to be able to match the subs to the satellites in phase and time.If this is not done you are likely to get more "punch" with the subs turned off! But matched up correctly and kick drum strikes come through with a reality that you can not get without subwoofers.
Subs also work best against walls and in corners. This placement increases their  efficiency up to 6 dB and minimizes room interactions. The satellites are usually farther out into the room. To match them up correctly the satellites need to be delayed about 0.3 ms (0.1 ms per foot)
The only way to do this is with digital bass management. Digital cross overs also can offer an infinite number of cross over choices with virtually no distortion. Room correction units usually come complete with digital bass management. Once you have this a whole world of subwoofer possibilities opens up. Now you can use a passive subwoofer with an out board amp. There are many subwoofer kits available for much less money and with minimal capability you can even build your own using the best drivers available. 
Once you have a properly dialed in subwoofer system there is no looking back. Systems without sound anemic. 
As an example, live rock concerts are held in large venus where bass can be produced very efficiently as there is much less room interaction. Getting bass like that in a small room requires the set up to be right on and a lot of power. My subs are always up 6 dB at 20 Hz  dropping to 0 dB at 100 Hz. This gain replicates what you hear in a large venue even with symphony orchestras. It also requires three times the power and if you are using room control up to 6 times the power. The effect brings big smiles when watching concert videos. Even with studio rock albums the added slam is appreciated. Instruments like acoustic bass are not affected because they do not go that low so there is no need to drop the bass for certain types of music.
Many if not most people would be better off spending their money on speakers that make better bass rather than subwoofers. In trying to make money on this concept the audio industry is short changing enthusiasts by trying to cheapen the product. IMHO the best approach to take if you want thunderous bass is to wait until you can afford at least two subwoofers and a good digital cross over.    

@rib61 - Looking at the Stereophile-measured FR of the JL Pulsars, the "knee" where the LF starts falling off is approximately 50-55Hz. This is a good starting point for setting the sub crossover. Then it’s just a matter of adjusting the sub’s gain/volume to provide the sound you’re looking for. The biggest mistake people make is setting the sub’s crossover too high, which mucks up the LF quality of the main speakers. Been there, done that with the result that you experienced.

I think that If you give the JL Audio E110 sub a fighting chance, it will reward you with a new and more enjoyable listening experience.

https://www.stereophile.com/content/joseph-audio-pulsar-loudspeaker-measurements

rlb61

As I said, I have a similar concern.   Most subwoofer users will say you should crossover fairly high, 80Hz being a typical recommendation.  Then, in passing those to a subwoofer that you can place optimally and/or DSP,  you get to refine the bass in the regions most affected by the room.

But speaker designers have worked hard on producing a certain character, and the Joseph speakers have this wonderful punchy, dense, "chewy" bass quality that I'd be loathe to give up.  Not sure I'd want to replace that character with whatever comes out of a subwoofer.

I also tried a REL-like set up using line level inputs, lower crossover points etc, just augmenting, and still couldn't get around the change of character in the sound of the main speakers when doing so.

@prof One of the things of concern is the issue of losing the character of the Pulsars by using the sub. For example, I've been advised repeatedly by some audio industry bigwigs to plug the rear port of the Pulsars when using the subwoofer xover. Well, I’ve tried that and it destroyed totally the sound of the speaker that I loved when I heard it at audio shows without a sub. I COULD simply run the Pulsars full range with the sub (and not use the internal xover), thereby just emphasizing the lower end a bit. However, that sort of defeats the purpose of the sub in the first place. I really think the small size of the room, coupled with the GIK room treatments, result in bass overload when using the sub.

@turnbowm ... I had the xover at around 60 Hz, so I don’t think I was mucking up the LF.