My concern is that you name several needs in your list. No 1 implement will ever address each.
Also your description raises a few questions that need to be answered to give you better recommendations.
The biggie in my opinion is regarding the roots and the rocks.
Are the roots small feeder roots or larger ground anchoring roots? Probably best able to answer this by estimating the diameter of the roots. Feeder roots are generally smaller less than 3” diameter with most being smaller than 2”. If roots are long and 3”+ diameter, they will probably have to be dug out, you may be able to do so with a stump bucket for the loader, but much less effectively than a backhoe. Small roots 1” or so can be dealt with with root rake or box blade.
You mention rocky clay soil. How large are your rocks? If large rocks (as much ad you want to lift by hand or bigger), you are again to possibly using a stump bucket, but better results with a backhoe. If drive base rocks and clay the the box blade or rear blade.
Working clay is tough—to wet and it balls up, baked dry in summer heat and concrete seems softer. If wet, live with its status, if baked you may make limited head way with a box blade with ‘teeth’.
Sticks and general debris, what do you want to do with it? Move it to a different location? A grapple! Push it to the edge and let it rot? Root rake or ratchet rake for your bucket.
Not the answer you want, but again no 1 implement is right for all jobs—why do you think so many implements are made?
Now let me made a plug for looking at used implements—most older implements are made heavier, they will typically out last you and your grandchildren, not to mention they may have already done that previously. Usually 1/2 or so of a new heavy duty implement. Unfortunately you seldom find a root rake (at least in good condition used). The bad, seldom are they QH compatible and some times not adaptable even if you have the ability to do the adaptions.
However, look into Pat’s QH for an alternative to the full QH, QH is extremely helpful when you have multiple implements and need to change with much frequency. 1 caution for PTO implements—all QH systems add 4+” in the needed length for the PTO shaft.