Basically I have been playing for a little while now and I play mostly Zappa stuff. I have a Made in Mexico Telecaster which is totally stock. I have a little birthday money at the moment and could afford to buy an SG (which he used loads.) Here are my issues though; I could only afford an Epiphone G-400 SG and I find SG guitars really uncomfortable to play compared to my telecaster.

I have used a tele the entire time I've been playing guitar. I love how it feels and I can play fast on the neck. As a result, the ideal thing for me would be if I could get the right sound by simply getting a humbucker put in my current guitar. It would be cheaper than buying another guitar and it'd feel better to play.

However, I find it hard to believe I could properly get the right sound without an SG or at least a Les Paul. I do have a wah pedal and proco rat to help though.

So yeah, can I really get a close Zappa tone with a Telecaster? I know these things are subjective but all advice is helpful.

frank used a variety of guitars and his main ones were often modified. he also used the best fx available at any given time as well as other quality gear. you'd have to be more specific as to what period zappa you are shooting for. just slapping a humbucker in your guitar won't do the trick for everything. as for the SG look for one with the 61 neck profile (ie Thin) which will be closer to your tele. I use a Vintage (maker not old) SG copy with the old specs and it is much more comfortable than the EPi you mentioned.
The thing about Zappa is that he didn't have one single identifiable tone his whole career. So it's hard to say what will get you "Zappa" tone. If you like One Size Fits All, look up the gear he was using during that time period.