I think you should apply the TRV by online because it's faster.
We applied for my TRV 28 Dec (at night) got approve 31 Dec(morning)
I only submitted the letter from by boss ,
my husband invitation(before b/f) to show how is your relationship with her and how do you gonna look after her for 2 weeks.
and more details.
Btw, I have US visa(maybe help)
Next step is PR (pray to Buddha )
Hope your g/f will get it