I had surgery ten years ago and it left me with some facial nerve damage on the left side of my mouth. It was necessary to make adjustments to my embouchure, but I still leak air out of the left corner during certain types of playing, i.e., high range, loud volume, double/triple tonguing. I like using Doug Elliott's mouthpieces with lexan rims, both standard and narrow. Has anyone had experience with very wide rims as a way of solving air leakage issues?

I haven't seen you play so it's difficult to make any suggestions, but I doubt a wide rim will help. A wide rim would allow you to press more, and that might firm things up a little, but it also might encourage bad habits too. Counterintuitively a thin rim in some cases helps firm things up! That's just an opinion and it wouldn't be difficult to get a Wide or a thin rim from Elliott to try. Wedge mouthpieces have a unique rim contour that said to help some embouchure issues, you could check out their website. Again I don't know if it would help but is something you could try.

A wide rim is worth a try... depending on other aspects of your face and mouthpiece placement. And/or a Skype lesson.

IMHO have a lesson with Doug.

I have 3 suggestions;

1) P.E.T.E - Personal Embouchure Training Exerciser

http://www.warburton-usa.com/index.php/pete

2) Caruso exercises - lots of ‘em!

https://www.markzauss.net/caruso6notes.html

http://www.julielandsman.com/gallery

3) Wedge mouthpiece

https://store.wedgemouthpiece.com

My situation is different than yours, but similar enough to share.

After playing about 16 years worth of live shows every weekend with Latin and R&B bands I found that I had a bit of a ‘hole’ in the middle of my tone. My playing was airy sounding when quiet and too aggressive when loud.

I tried Caruso‘s which were heading in the right direction but not producing results fast enough.

One day while discussing my problem with a colleague he mentioned that perhaps I have a bit of a spread in my Embouchure. This really got me thinking! So after some research I came across the PETE trainer. I bought one right away and it solve my problem in about three days. I couldn’t believe it!

I have a nice tight buzz again and my beautiful sweet sound is back. Control in my middle, high and extreme high register is better than it’s ever been. I can play ballads better than ever and even sound a lot like Bill Watrous.

I hardly use the tool anymore but the results have remained. I go back to once in a while because it’s great for endurance and staying on top of things.

My First choice is the PETE. You can use it to tighten up your buzz in the centre of your embouchure as well as improve your endurance.

In your case, I don’t think it would do any harm to use this tool ‘off-center’ from your main embouchure to train your weak muscles to behave without any negative results.

Hope this helps