Subwoofers driving me nuts

Are your mains on the long wall or short? Swap your speakers and see what happens.

As dweller said/implied - your speaker orientation has the biggest impact in your overall sound. One should always try orient your speakers along the long axis of the room. Sometimes that isn't possible (The CFO booted me out of my former room into a 'larger' 12' by 12' space. That being said, if you are already going along the long wall, have you tried to change the angle of the sub? I have my Infinity BU-1 firing into the corner of my room behind my Infinity 6 Kappa speakers. With sub woofers, there is a lot of trial and error. A lot!

If you have a favorite CD recording, one that you know particularly well, count on playing it a few times, especially on low-end heavy portions to dial in your sub-woofer position.

What you describe is of course physically impossible. Bass travels in waves of different lengths at different frequencies. Its possible to have nulls of no bass at certain frequencies, in fact not only possible but guaranteed. But it is impossible to have nulls of no bass at all frequencies. This is step one in understanding your problem.

Step two is your room. But keep in mind all rooms have this same problem to some extent. Your dimensions 13x21, the width is very close to the wavelength at 80 Hz which is 14 feet. You can play around and find the exact bass frequency at 13 feet it will be a little higher but whatever. Point is to start thinking about it as a problem in math or geometry. 13 and 21, seven is close to a common denominator. The worst room would be where they are all multiples of each other 24x32x8 for example. 

You have moved them around a lot. Welcome to the club. With only one or two subs that is all you can do. It never will work but its all you have with only one or two. My guess is you also are following the conventional wisdom and moving them symmetrically. Because someone repeated the line about integrating, or timing, or whatever. 

What you want to do with your two is put one in a corner and move the other somewhere very different, like a side wall several feet from a corner. This way you will have two sets of very different bass modes and nulls, and the overall response will be smoother.

You never will by the way get as much bass in the middle of the room as along a wall. Any wall. Any system. Any room. It just ain't happening. You don't even want it to happen! What you want is smooth even bass at wherever you're listening from. 

All the advice above is ultimately little more than a here's how to make it a little less crappy type solution. For really good bass nothing with only 2 subs is gonna get you there. For that you need two more. At least.
https://systems.audiogon.com/systems/8367

Have you done the subwoofer crawl with a sub at the listening chair - as shown here?

its worked for me

Placement + Bass traps. I recommend the Soffit Traps from GIK acoustics.

Try adjusting the phase relationship of the subwoofer to the mains.  Could be sub is substantially out of phase and cancelling at various frequencies in the low octaves.  While there is no exact solution either physically or in time (phase) in a room where there are thousands of reflections you may be able to minimize the cancellation and create a better overall balance.  To "see" what is going on I recommend using a spectrum analyzer, preferably one with constant percentage bandwidth filters, 1/3 octave minimum or 1/24 octave is better.  Very narrow band usually labeled FFT spectrum is also useful but can get confusing.  There are a number of free programs out there that work great for analyzing room acoustics.  Below is a link to some of the best I have found.  I think you will enjoy being able to see a little bit of what's going on and correlate that with your subjective impression.  Once you get a picture of what the room and speakers are doing you can try some of the many corrective solutions that are available.  Let us know how it goes.    
https://listoffreeware.com/free-audio-spectrum-analyzer-software-windows/
 

I can't hear the issue, that's the problem, right?  You have any room treatment, at all?  If you could get your position closer to a back wall, then treat the wall behind you. Normally  further from the speakers, the deeper the bass, to a point. Speakers 4-8 foot from (their) rear wall, 2-4 ft. from sides. Your position 8-12" from mains and 4 feet from your BACK, not the middle of the room.
French doors, sound like a bad idea, until they are opened on a back wall, behind the listening position. 
The BASS, escapes, not reflects. The wall behind the speakers is very, important, every wall has an issue, the more you can tame (or get rid of), the more you can hear.  If you can't kill let the sound escape, you have to use it, "reflex bass".
The only thing left at that point is measure and EQ, HUGE bumps, and that will take care of some of the NULLS. Then EQ up to where you need. In the setting position. If your trying to get bass on a dance floor, that's different too, four TOP corners, pointing down on the floor. or NO BASS.

If you can;  mains at 40-60hz and above, subs go from there down. THEN you'll probably start to hear more than one note, and bass.
Most people have their subs set WAY to high, Sub is actually what you CAN'T hear only feel. SUB.. You got to much of a GOOD thing.. I'm at 50 hz and down on two subs, and 35-40 hz and down on the others (2-4). ALL are cut at 20 and below. (glass is expensive).

Regards

Since the swarm-is-the-rage, I'm wondering how this config would sound: A 15-18 sub (single) in the middle, two 12s (left and right), and two 8-10s (further left and right). Another reason to play the lottery!

In my 28 year listening experience, I've never used more than one sub. I'm currently using a 20 year-old B&W ASW650 (lit says 12 inch but more 10-11 inch) in my smaller room (12 X 13). Listened to Joni Mitchell's intro to "Cotton Avenue" recently and Jaco's bass was "all there" which is good enough for me. 

Good luck with you project! 

Miller, thanks for the idea.  I've been struggling to get my two subs correct and I moved one  down the side wall almost to my position, adjusted the delay and when I adjusted phase on the odd one to 120 degree to account for distance it just clicked. They vanished and I can not locate them. I would have never thought of placing them in an unrelated position.  Much obliged....