Based on what *very* little I know about IP Unnumbered, I don't think your route changes are related to this (my impression of IPUnnumbered is to share an IP with another interface on the same device, and that you specify which IP address you're "sharing" at configuration time).
Route oscillation is a relatively normal thing (and it is becoming more and more normal). If a single hop is oscillating between two different routers, just right-click that hop in the upper graph and select the "Add Route Change Mask" option. Then reset your trace session (right-click the Stop/Resume button, select Reset and Restart). Future oscillation on that route shouldn't cause an identified route change (although you can watch the IP address reported on that hop chagne dynamically, Ping Plotter won't log it to the route change log).
If you're not seeing normal oscillation, feel free to post some pictures of your multiple routes and we'll try to comment on it.
- Pete