Nice to see this forum knows you're getting engaged. Does your girlfriend? Perhps it's a generational thing but I'd have thought she'd be the first to know, and that it would be a surprise....?
I'd keep the car, as as life goes on it will likely yield you less opportunities for such things, unless you do well, which you may, and you may not. If ownership means you're begging favours i.e. keeping the car in your parents garage then unfortunately you're going to have to consider their opinions on the matter.
Forget chasing 11s would also be my advice. Be happy you have a GTR and use the 11s fund to invest, provide for the future of your relationship and inevitable offspring.
Good luck either way.