I find that they pretty much have to drag against the floor to be useful.
Yep they normally do... If it going to be on a flat surface then it would be ok. I would just gut a better mouse (a microsoft optical probably as they can run in ps/2 mode)
If it is going to be in that room then you could use more ultrasonic sensors...
If it's outside then perhaps the distance measuring doesn't have to be anywhere near as accurate and a GPS would do... The SIRF III chipset can be accurate to about 2.5m (massive distance indoors)...
What is the project for? If you can explain exactly why you want to measure the distance travelled then I could probably give some better answers but we're currently working in the dark here...
Mowcius