For repair bit, every +1str+1tec increases duration by 0.5 secs and vice versa (that's after some tests from between 4tec/4str up to 18tec/18str, some said that the increase stops being linear after a certain threshold but I'm unable to confirm that), so it's not a huge increase. It also improves HP of the bit but that hardly matters unless you are being hardcore and trying to play a frontline combat healer/HSer.
Fly works fine, it's permanent high movement speed from walk versus short burst of higher movement speed from fly, as a support, you'll probably find that the latter works out better for you, and it helps you avoid some melee.
As a healer, you don't really need extremely high mobility. Depends on what base stats you got, try aim for a break point with WLK or FLY, 22 is a pretty ideal movement stats to sit on, if you can reach it, all well and good. Though what you should do is prioritize cartridges over stats, leave the tuning secondary. As long as you have 10 str 10 tec, you are set for life in terms of stats, better movement speed is very much a luxury.