Goedjn writes:
Well, when it is clogged, I have tried filling the bowl to the brim
(which should be as good as a bucket full, right?). Some of the time
the extra head of pressure clears it but most of the time I still need
the trusty plunger.

If you are saying that I should try the bucket *before* I get a clog,
how will I know whether the bucket helped or whether it would not have
clogged anyway?

Ok, I think you have successfully demonstrated that the problem
is *NOT* insufficient flow from the tank to the bowl.

One more "interesting" observation.
Sometimes when flushing, the solids will first appear to go down the
trap, then "regurgitate" up into the bowl and then drain back down
again. This does not always happen.

Does this indicate anything?