Unlike wood pellets in a small burner, there are a lot of variables in a natural-wood-fired TLUD that you can't possibly fully control.
If you clamp on with a big vise-grip and shake the barrel hard, that may well re-establish the flow. The simplest solutions are often the best.
Inserting two chunks of rebar, bashed into a crude auger (helix) shape as you load would let you pull or twist the mass at will.
If you inserted a perforated full-length pipe down the middle, with a cap on top, as a precaution, you could quickly re-establish strong draft top-to-bottom to limit smoke.
Just some ideas.
