"3. Can I cut it all the way to the ground and start over?"

Yes; that's better than cutting just part-way back, too.

Resin

If the falling flower petals cause you problems in the area where the tree is growing, then get rid of it and redesign a more appropriate landscaping for the area.

If you want to save the tree, but do not feel it can now be pruned appropriately; then wait till it goes dormant and cut the trunks down as you described above. Dig up the remaining roots; then, replant the stump in an area where falling flower petals will not bother you and where the potential height growth of the tree will not be a problem.

Then, let the number of desired new trunks grow, and once thick enough to survive the winter, prune them. Just, please, avoid using the crape myrtle murder type pruning method.