Back in the 90's, I remember someone who had two little BMX levers mounted backwards on his aerobars. If your guy only wants one, which one? Rear only will lock up, front only I don't want to think about!

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''Sweeney - you can both crush your AG *and* cruise in dead last!! 😂 '' Murphy's Law

I get the adage of "The customer is always right" but in this case I feel like putting a third brake on the bike is only enabling poor behavior. I would say that he would be better served by learning how to get more comfortable in aero or learning how to quickly jump one hand over to the brake to slow down.

The guy probably looks to you as his bike expert in all areas (even riding) & while you may not be a coach or a riding instructor, you could hopefully sway his decision & help lay some of his fears to rest.

Something like a cyclocross brake lever could work with some modification. They are installed mid-cable and work by effectively lengthening the housing similar to an inline barrel adjuster. The problem is that they'll be made to fit either a 31.8 or 26.0 bar, not the 22.2 aero extension. If you can work out the bar clamp problem then the brake run would be straightforward: run compressionless housing out one extension, through the inline lever, loop back the other extension and continue to the brake. You would also need an extra long cable as would be used on a tandem due to the extra housing loop.

+1 on the teaching bad techniques.
Out here in the mountains of southern oregon, you HAVE to master descents. If you're not super confident, do the old left hand on the extensions, right hand on the breaks, technique. I see alot of other tri geeks doing the same around turns. (Which is probably improper technique in itself! )
Also, I've seen a guy who put a 3rd break on the right extension. He used an old BMX style break. He put a whole second set of breaks on the thing though.