I have a Woods 750 3PH backhoe on a MF1020 and have had no rattling issues. I noticed, however, in your pic that there could be some play in the attachment to the 3PH arms. I have large washers on either side of the two pins, so there is no lateral play. I have removed a number of stumps, dug ditches, holes, etc. with no problems.
OT. Also, to remove/install the BH unit, I built a T-shaped dolly from 2X8's. At the ends are ($7 ea. on sale) 1,000 lb limit dollys from Harbor Freight. I also attached vertical boards at each "corner" and mounted trailer hitch crank operated jacks ($20 ea. on sale at Northern Tool), so that I can raise/lower any corner. The "bucket end" (when crank lowered/raised) takes the pressure off the top link bar. After removal, I just wheel it in the corner of the garage!