I'm really having a hard time envisioning a bucket grapple stuffing a chip. The bmg can drag whatever the capacity of the machine it's on will handle. I drag backwards to the tray, turn the machine 90-180 as I'm near the tray and if you've grabbed the butts long enough you just jam them into the feed wheels. One man chipping never get off the machine.
We always have a man at the chipper to raise the upper feed wheel and do whatever needs doing near the chipper.
Feeding with a bucket grapple and artic wheel loader is very effective. The most obvious way is to bite the brush/leaders/logs sideways (as in perpendicular to their long axis) and drive them to the chipper and feed them with the loader roughly perpendicular to the chipper. When space constraints prevent sideways feeding or carrying, all brushy tree parts can be grabbed in the middle and carried and fed with the butt ends quartering away from or quartering towards the loader, rather than the material being perpendicular to the loader. So the machine approaches and feeds the chipper being nearly in line with it. Typically, brushy leaders are carried with the butts out front and tips behind, and fed while driving forward. In your scenario above, if you wanted to feed the chipper while traveling backwards, you grab the material so it is quartering to the machine, with the butts sticking well rear of the bucket and tips sticking forward and drive backwards by the chipper as the butt ends go into the feed wheels, no turning 180 needed. Logs are carried and fed sideways, lengthwise, or quartering.
Rakings piles were mentioned above; the bucket is excellent for removing multiple large piles at a time, leaving a barrel to handle occasional small piles that crop up.
Occasionally, we will grab or choke smaller trees that are just inside a pool fence for example, or where there is no room to fall the tree, cut them and lift/ carry them vertically, feller-buncher style.
With a grapple, can long brushy leaders be carried and fed butt-first while driving forward to the chipper? If the tips are brushy and flimsy as is normal, what does the heel bar push on to get the butts up in the air?