V-strom with knobbies should be fine. 95% of the road to Toroweap is smooth gravel/dirt. Some double track and a few rock ledges (small) near the overlook, also 1-2 silt beds. If you go slowly where prudent you won't have any issues.
Post #92 near the top of Page 7 has Toroweap pics, but none of the 1 or 2 bumpier sections.
The V-strom will be ideal for the fast stretches and the slab from Colorado City back to St. George.
If you have gone even a few miles past the end of Navajo Drive then you've been on worse roads than almost all of the Toroweap ride.
Worst case scenario, you can always stop or turn-around.
Hope you can make it. Oh, and welcome to St. G.