I`ve never had a Mallory that worked correctly. I swapped out the last one with a points dist with a Pertronix conversion. Glad you got it up and running.
"When it quits, the tach drops like it was disconnected even though the engine is still spinning." That is a Pretty powerful symptom pointing to ignition. When my turbocharged Corvair's tach wavered the slightest bit I knew it was to re-gap (and clean) the points.
An interesting post-script to this problem. The coil died today. Now I suspect that the coil caused the Unilite to blow. In any case, I have the old GM style can coil in it now, and with the points distributor it runs great. No more electronic stuff for me, unless it is a GM HEI, which unfortunately will not fit without firewall mods.