NH TC21:
TractorData.com New Holland TC21 tractor information
I have cleared quite a lot of similar jungle in Florida. I used a Kubota B3300SU =
You are asking a lot from a subcompact 20-hp tractor with 10" of ground clearance.
First off BE CAREFUL. It is all too easy to topple a light tractor when applying force.
A Ratchet Rake for your bucket, in addition to the Tooth Bar you already have would be my first suggestion.
Ratchet Rakes are sold by the T-B-N stores.
RATCHET RAKE VIDEOS:
https://www.youtube.com/results?search_query=ratchet+rake+brush+clearing
After knocking down brush and saplings with the Ratchet Rake a Rotary Cutter (Bush Hog brand or other brand) will chop up vegetation.
I had a 48" King Cutter (brand) Rotary Cutter that was indestructible. You need a fairly heavy R/C by weight as you will often push it into brush in reverse, so the tail when and tail wheel mounting takes a beating. Light weight R/Cs, made for mowing pastures, will break.
To pull out roots, wild rose corms, Smilax and grape vines under the surface a Field Cultivator is the best implement. The tines are 3/4" wide so they pull relatively easy. You would have to buy a five tine model. You would have to remove one or two tines. You can pull three tines in moist soil, possibly four tines.
With the Ratchet Rake you can then pile the debris. There will be a lot of debris.