My concern is that no new shoots will develop
after cutting down to the ground.

Don't worry. If you cut your oldest, thickest canes back to about 4 inches, you
should have new growth to a height of 2-3 feet in the next season. The new
canes will not bloom until the season after that. See:
http://www.colostate.edu/Depts/CoopE...ubs/lilacs.htm
sed5555