I agree, TT is too small. Do you think going from a 605 to a 650TT would be too much of a jump?
You also need to work out the relationship with the seat/bars. You mentioned that the seat was as far back as possible, so if that moved forward 10mm, and you ran a shorter stem (say 80mm) you’re real TT has moved from 605mm to 635mm, so now only a 15mm increase.
But tbh once you ride the right size you’ll suddenly realise the difference it makes, IME the ability to climb and put effort in as you are able to ‘open’ up you chest – different world.
+1 proper bike fit – there use to be a US based website where you could put in all your dimensions and it would recommend frame/fit dimensions. Here you go:
http://www.competitivecyclist.com/za/CCY?PAGE=FIT_CALCULATOR_INTRO
I found it after I’d got my bike right, and then on measuring it was pretty near to where I’d got to 🙂