I have some experience in brush removal. My opinion, if you can poison the brush before clearing, you will have better results. Foliar herbicide application needs the maximum plant foliage to deliver enough chemical to the roots and thus kill the roots and all. You can also treat cut stumps, but that is fairly easy with larger trees and brush, but harder with smaller plants to get an efficient coverage. I think professionals usually spray in fall to take advantage of this. Once dead, I have used a saw to cut anything 3" and up and have a tractor with rotary cutter to do the rest. There will be some brush that survives (guessing 10-15% ) that you can do follow up treatment the next year.
Remedy ultra is what I have used for this. Works on the species I have, but is not universally effective for cedar, and other species. Not sure what you have to eliminate, but there are some effective herbicides that can be purchased without a private applicators license.
May not be feasible depending on the size of area you are wanting to treat, the thickness, etc. but maybe worth consideration.