Good, affordable pathway materials for sidewalk with tree root problems
Depending on where you live, reclaimed brick can be very inexpensive. The same theory still applies: if there's a problem in the future, just pull up the bricks and re-level the bed. However, bricks are thicker than bluestone, so will you have less stone/sand between the brick and the roots, and thus less room for adjustment.

Another possibility is just moving the walkway. If you're going to re-do it to deal with roots, why not run the walkway in a different spot?