Hello there John.
First off, on getting the remote apart, you will most likely damage the speed control knob if you are not very, very careful, as it is made of a soft plastic that will deform a little as you pry the knob off. you might try pulling it off with pliers with some soft cloth over the jaws, but I had the best luck using two small, flat screwdrivers from either side. What is hanging you up is a nut that is under the knob that secures the shaft of the potentiometer to the remote's shell. Once the knob has been pulled off, it should be easy to remove that nut.
On the circuit, I have not done what you are suggesting, but I have torn into a remote for another project and don't see why it couldn't be done... though there is relatively little space in the remote for additional circuits. It is also important to note that the remote's electronics run at 3.3 volts, so that may or may not be an issue.
The short of it is, if I recall correctly the buttons are activated by a low (0 volt) pulse, so you would need a circuit that can detect when the button is pressed, then some time after that signal, say 20 seconds, produce another low pulse on the button. To fit in the remote and run off of its power I think this could best be achieved with a small PIC microcontroller, but I'm afraid I', inexperienced with those. doing this myself, I would use an arduino-type board, perhaps a "tiny" or a pro-mini if it can be shoehorned into the remote.
Another option that comes to mind is to use one of the esp8266 Wifi boards for 99 cents. these can be programed to perform simple microcontroller code, but is once again a bit beyond my current knowledge.
Over all, I'd say it is perfectly reasonable to think what you want CAN be done, it is mostly a matter of the available space in the remote for an additional circuit. If there is room for a 3.3v pro-mini, I'd be happy to write the code for you and explain further how to set it up. If there is not room, then it will take some more thought as to how to do this.
Feel free to email me or write back here, and if it sounds like you want to go forward, I'll pull apart a remote and check the clearances to see what we can fit in there.
Here is what I've done with the remote in my project:
JGL
Johngaltline@comcast.net.
