Although I haven't used these parts, I want you to look here, here and here.
**broken link removed**,
www.cpustick.com,
www.comfilech.com
The first uses the CPUSTICK OS. The last is BASIC. You can download an emulator for the CPUSTICK OS.
With all you have to do, I really don't suggest a bunch of timers. A general purpose CPU, I think makes more sense.
With a few H bridges and some High side current measuring IC's and probably some inputs and your there. You could add an LCD easily with the BASIC module and go from there. You could try the straight timer mode, but you could add a RESET mode, where the system would go toward a limit. Stop, reverse direction and go to the requested position. Limits could easily be achieved and it would solve all of your problems except perfect positioning.
The way systems are designed is you have two limit switches and an ORIGIN switch. The ORIGIN switch is very precise. The idea is that the system heads toward the org switch, passes it, stops, reverses and SLOWLY moves until ORG is found and stops. With steppers, you can pulse the required number of times. Servo motors require n encoder.
Any way, I'd bite the bullet and go for a processor based approach. Those three don't seem hard and they don't require a development kit. The hard part will be getting everything to move at once. When I did a gantry crane for a model railroad using the 1802 processor, it was nearly impossible to get both axis to move at once. I was able to do so using BASIC. This was 30+ years ago.