As a temporary solution, I would suggest using the 994 method to assign some more harmless key, like the down arrow, to the menu button. If you don't know how to do this, first press the correct device key, then enter the following:
SETUP*_**9*9*4**DOWN*MENU**
I'm assuming that you know the standard shorthand for these things, which is to say that * represents one blink of the LED, and that SETUP*_** means "HOLD down the setup key until you see those two blinks. (**)
This is only meant to be temporary. You could do better by using a similar method to assign the actual menu function to the key, but you'd need to know what number represents that function. One way is to request the advanced codes for your device from UEI, but I wouldn't hold my breath if I were you.
Another way is to figure them out yourself. You risk sending your device into some sort of "factory mode" if you do this, but it wasn't a problem for me, and I figured out the codes for three devices by trial and error. (One code sent one into a "factory mode", but sending the same code again got it back out.)
If I had a digitized sample of your menu button from your original remote, since I already know what device code works with your device, I could probably tell you the advanced code that would send that signal within 24 hours. Unfortunately, no one has taken me up on this idea before because no one else seems to have the technical skill and inclination to digitize the remote signal.