The suggestions I've received have been incredible. You guys are
excellent troubleshooters. Thank you so much.

Update: The more I thought about it the more I became suspicious of
that coil. I took the boat out last night and parked it on the
street. I fired it up in the dark and looked for any sign of
crossfiring or voltage leaking. It took a while, but once the engine
was hot, the coil began to ark to the block randomly. In fact, the
whole coil had a faint blue glow with occassional sparks jumping to
ground, coming from what looked like right through the resin body.
This is the familiar "late model" HEI system with external coil of
somewhat square shape that Mercruiser bolts right to the intake
manifold just in front of the distributor. The engine didn't miss,
but as we all know these ignition problems are worse under load which
I can't duplicate in my driveway! My theory is that this voltage leak
probably gets worse as the coil heats up, causes insufficient
secondary voltage and either 1) a compensatory increase in secondary
current (remember Ohm's Law?) which will burn the cap terminals and/or
2) random sparking which is not appropriately timed with the rotor/cap
alignment causing both the burning effect and the tach error. I put a
new coil on it today and did the same night time test and saw no
arcing and no glowing. I feel it is very likely that this is the
problem...a coil. I've experienced failing coils at one time or
another, but never with symptoms like this. I'll post a follow up
when I have a chance to get it out on the lake and test it, but it may
be a few weeks. Thanks again to all who chimed in.