That's a lot of motion for a mechanically coupled solution to handle on the cheap. LVDTs are available with insane ruggedness, but they cost quite a bit. I'm not sure if the low end LVDTs would hold up, but they might be just fine. The ruggedness of any approach can be very good. An LVDT will have little trouble with dust or debris if it's bolted to the shaft (most are designed this way). An optical solution is more vulnerable, but is likely to be a lot cheaper and have no problems with wear.
What information do you need? Just the peak time on the shaft (high and low), zero crossing, or do you really need 0.1mm analog accuracy on the complete travel?
The expense of the good linear displacement sensors comes in making it linear and accurate. If you don't need the median values you can save a lot of money.
Do you have transverse access to both resting points?
If so, optical interrupters might be a good idea, either hooded IR or laser. You can use interpolation in software to estimate median values if you need them. If you're not using a micro, well, it might be cheaper to put one in than to get a good sensor.