"On paper it looks great. It has dedicated graphics so the graphics essentially run off of the processor."
It's not dedicated. That's integrated. There's actually no physical card in the computer. The GPU is built onto the CPU die itself.
" I've been told I can't change the card on this computer, but I need more verification. Is there ANY way under the sun to upgrade this card? "
Unfortunately, what you have is an ultrabook that has no provisions for video card upgrades at all.
"Can I take it to a computer repair store and have them find a good one to fit my computer and install it for me?"
No, there's nowhere to even put a discrete card in that computer.
" Can I get some sort of external device that might plug in through my USB port to boost my graphics?"
Nope, USB is far too slow to handle the bandwidth needs of a discrete video card.
"Any method that can take this from an amazingly high-spec pile of useless junk to the most effectively economic saavy gaming machine ever made?"
Nope, If you had a Thunderbolt port on it, then there would've been some hope, but unfortunately your computer lacks that.