What degree/major would someone want to look into if you were interested in trying to work for an amp or pedal company? Maybe electrical engineering? I'm really interested in this type of work but is it a field that is near impossible to get into? Is there anyone on the forum who does this that maybe I could talk to more about?
I think EE would probably be closest, but you would still have to do more learning about it on your own. EE would give some electronics know-how that would benefit you, but the curriculum almost certainly would not cover most necessary things for breaking into that field.

First, I presume you are most interested in tube amps. Tubes are an obsolete technology. No curriculum is going to cover how they function because it is such a niche topic since the invention of the transistor. Also, (this also applies to solid state amps) courses will be focusing on how to not distort the signal, which is often the opposite of the desired affect in amps/pedals.

You might learn about a couple topics related to pedals commonly used, but again you would mostly be learning how to avoid these affects in more common circuitry.

EE also has a heavy programming focus nowadays, since computers are kind of important most everything electronic anymore. This might be helpful if you go the digital route.

Basically, what I'm getting at is that it will help, but you will have to do a lot of learning on your own to apply it to that field. As far as choice of major though, that's probably the best place to start if you want a degree that's related in any way.

I can't really comment on the difficulty of breaking into the field.
Well I think it would make sense that the top two have backrounds in electronics engineering! I'd really like to have a conversation with someone who currently works in that field. Is there anyone on the board who works for an amp or pedal making company?