Would increasing pipe size just after the meter give better flow without increasing pressure too much?
Bad idea.  Enlarging hot water lines will dramatically increase the inventory of water sitting in those lines.  I.e. How much water is in the lines themselves.  

I.e. How much cold water those hot water lines are full of, when you first turn on the shower.  

I.e. How long you must wait for the cold water to be pushed through and become hot. 

You reduce droops by not allowing any one appliance to suck up all the water, and you do that with flow restrictions.  The single best thing you can do to ease water droop is fit low-flow showerheads.  Of course, if it's a shower only, with no tub diverter, that means waiting even longer for initial hot water. 

Here's how I'd fix that.  So I would couple that with minimizing the size of the water pipes, and have a homerun for each shower, for both hot and cold lines.  And tap both right at the top of the water heater.  That will ease pressure droops, and pressure droops will affect both hot and cold equally, so no chilly/scalding surges. 

So for instance a 3/8" run just for each shower.  A 3/8" pipe has 1/4 the inventory of a 3/4" pipe, so it warms up 4 times faster.  Such a small pipe would make sense given your high water pressure and a low-flow head.