yeas a forester rotary cutter will grind them down flush with the ground
but, WHY spend the money renting one, not to mention they can be pretty aggressive to get on the ground smooth like as they hit and toss things! and why most true machines have thick glass /cages on doors and such rated for impacts from things!
SO?
If you have access to a skid steer now right??
why not just cover things with stone or dirt, as odds are that can be had on site from near things,, IF by chance anything starts to grow thru, just hit it with brush killer spray,
OR pending your need to have done, if you let them thing DRY out, you can simply push them flat with a bucket, they will shear off when there dried out, like breaking a dry stick
and a last option, is, you can also try running things over the OTHER way with the brush cutter you have, or raising and lowering it on things,
as when you use a brush hog type mower on a skid steer, things tend to get pushed /folded over, thus NOT allowing things to all get cut,
but if you RAISE the cutter and lower it on top of things,(boom up, then lower on them) it will cut them lower, NOT flush to the ground, but will cut them lower than what you have
you just need to first straighten them out again, but pushing the other way slightly
this might be more time consuming than one wants to do, but does get you a lower cut on them!
me, I'd just bury them, as right now there LOW spots and as such they will also hold water making puddles and soft spots
so filling them in will kill two birds with 1 stone, by getting rid of future mud holes and getting rid of the tire pokers at same time!