An update for you all: this is now working well, after a year of neglect and some redesign!
I ended up needing to redo the actual mount for the servo to eliminate binding. I also had to modify the software I was using to control the servo.
Here is the batch file I ended up with:
if "%1"=="90" goto vert
:horiz
d:\Utilities\Pololu\Maestro\bin\usccmd.exe --servo 0,3456
start /wait d:\Utilities\Pololu\Maestro\bin\usccmd.exe --accel 0,0
start /wait d:\Utilities\Pololu\Maestro\bin\usccmd.exe --speed 0,30
d:\Utilities\Pololu\Maestro\bin\usccmd.exe --servo 0,7680
goto end
:vert
d:\Utilities\Pololu\Maestro\bin\usccmd.exe --servo 0,7680
start /wait d:\Utilities\Pololu\Maestro\bin\usccmd.exe --accel 0,0
start /wait d:\Utilities\Pololu\Maestro\bin\usccmd.exe --speed 0,30
d:\Utilities\Pololu\Maestro\bin\usccmd.exe --servo 0,3456
:end
timeout /t 2 /nobreak
d:\Utilities\Pololu\Maestro\bin\usccmd.exe --servo 0,0
exit
This code turns the servo off entirely between rotations. The servo therefore loses its memory of where it was; that's why it issues the command to take it to where it already is first. Given its current location, the speed and acceleration commands are then possible, because it apparently uses the distance between the two servo positions to calculate the movement curve on the fly. If you don't set the servo to current position after turning it off, speed and acceleration will instead be at maximum, and this will throw the monitor really hard, causing bounce at the far end of travel, likely torque damage to the servo, and probably loosening the mount.
I have a magnet at the far end of travel and a homemade latch to hold the monitor in the right vertical position; on the horizontal I just use a small rubber bumper disc, because the weight of the monitor wants to turn that way anyway. These are both hit by a physical stop I built onto the back of the bumper plate. I tried a magnet latch there and it was actually too strong! I do have some weaker magnets, so may try this again at some point.
Given the much better mount with no binding, I was able to make this work with my original HiTec 645MG servo. Which is good, because the other servo I got needed 7.4V and could draw spikes of 8A, way over what my 6V/3A wallwart could supply.
Once I get some photos uploaded, I will post the full details of the mount for the servo.