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?