Hey buddy, sending support from Scotland! I'm afraid the GICs all over the country are pretty much the same in terms of waiting times, it's awful...
I just wanted to point out that it's easier than you think to get your name and gender changed on your passport and drivers licence (not much less expensive, though)! For the passport, you can use a GRC as a proof of gender change, but you can also just send them your deed poll and a doctors note (saying you'll be this gender for the rest of your life blah blah). I think it's about £80 for a new passport, but don't quote me.
As for the licence, you don't actually need to change your gender at all. The way the licences work is they have like a special "code" for male and female - they change around the numbers in your Driver Number (i think that's what it's called?) depending on whether you're "male" or "female", it doesn't explicitly say your gender anywhere on the licence. I just changed my name on my licence by sending my deed poll, didn't see the need to change the gender as no one would notice unless they knew the code!
Hope that's helped you in some way, all the best!
Aaron