Yes, I'm sure what you want could be done. You would have to check with Everlast about warranty issues. I would guess that you would be on your own there, as you might be able to mess things up. If the warranty is important to you, I'd stop as you mentioned that you don't have a lot of experience.
You can change the way the pot works, but it's a bit beyond the scope of forum posts. You would have to reverse engineer what is going on and you might have to open up the welder to get that info. I'm not even completely sure that just opening the pedal sense pins takes everything out of circuit. It might take out the panel amperage but leave the pedal parts in circuit, that could make your adjustments strange or non-functional. You have to think about the original design. The purpose of those pins is to bypass the panel control and route it to the pedal. A little testing would be required to determine that the reverse is true. So you might need a few more contacts on your switch to get the job done. I believe someone has done a breakout box like you mentioned, but I'm not sure for what model welder. You can search the forum for more info. It would be handy if switching to stick mode bypassed the pedal. However, I have stick welded once using a foot pedal for fine amp control. I was filling in a varying gap from a bunch of previously torch cut pieces way up under a roof where I really couldn't do much to improve the fit. The only machine available was a TIG and it turned out having the foot amp was kinda cool. HF start was nice, too. Just another tool in your belt for the odd job. I know Miller has a belt mounted wireless remote amp for pipeline stick welders so you don't have to climb out of a trench to switch your machine.
Long arc, short arc, heliarc and in-the-dark!