Road-racing bikes use the 130mm rear axle, yep.
Part of your speed increase is due to the lower air drag
of not having racks, fenders, panniers and wide tires, not just the lower weight alone. You may already have reached the point of diminishing returns without spending much money yet
If your back weren't an issue, then an aero bar might be worth trying, because it helps streamline the rider, who's the majority of the air drag. And air drag is what slows you down most when you're on a steady cruise.
If you do try aero bars, get ones where the armrests are behind
the main handlebar, not right over it, and consider using a shorter, taller stem if you find you're too hunched-down. Also, leave a big buffer of space around you since they make the bike steer differently when you're down on them. Worst-case scenario, you can unbolt them and sell them off to your pals if they don't work out.
Syntace C2 Ultralight
, I have a set of these.
For me, the aero bars give 1-2mph boost when I'm just cruising the highway, with no additional work, and I just sort of drape myself between the seat and bars and relax my back. That's a bigger boost in speed than my exotic $1200 all-carbon Zipp440 tubular wheelset was, back in the day, and for a bargain price of ~$100. Although those Zipps were wicked-cool and accelerated really well...