I know this has been discussed before, and I've done a lot of reading
about this problem and some troubleshooting. I'm almost ready to
throw the toilets out and buy new ones.

I've been in the house for over 1 year, and the two toilets on the
main floor clog at least 50% of the time when
flushing solids. When flushing only water, it's never a problem.
Both toilets are Mansfield from about 1978. The tanks of both fill up
to the dip tube, and there is nothing in the tank to use up space to
save water. I've poured 1/2 gal of muriatic acid down the dip tube to
clear out the water jets, which didn't seem to be clogged at all to
begin with (I tried a piece of wire first). These toilets don't have
the large water jet at the very bottom.

They're on a city sewer, and I don't notice any other odd symptoms
like gurgling sinks. However, one of them is a little loose on the
mount, but there's no water leaking. It's rare for the clog to occur
inside the trap; it almost always clogs within view right at the drain
hole entry. This makes me think there isn't anything stuck in the
trap, although I haven't discounted this possibility.

Any ideas before I throw them out?!