On a related note, I have a transformer from Radio Shack (The Source) that's about 3-4 inches long... you plug a 1/4 inch and it's end is 1/4-inch. When I use that in the guitar (along with the G10T) it works fine without any high-pitched hum. And so, although a bit of a long thing sticking out, it works.
Yes, the guitar does have a TRS... it includes a cable that allows you to split the signal to two different amps.