Ted -
A few things -
A "normal" alternator relies on an external source for "excitation" voltage, which is the "second wire". A single wire alternator draws its excitation voltage internally, thus only requires the one main connector wire, thus "single wire". Some single wire units on the market are conversions, they just add a jumper to the voltage regulator. (You probably already know all this)
I and some friends have bought several inexpensive aftermarket "mini Denso single wire" alternators. They've been cheap Chinese copies of a Denso alternator, modified by the reseller to be "single wire". Our luck with these has been terrible, I've had them last less than one race weekend before. The problem seems to be vibration, I've run underdrive pulleys so the actual RPM is not severe. The failure mode n mine has been the stator windings actually vibrating loose and moving inside the case, severing the wiring. Last go around I had a local electric rebuilder take the unit apart from new and "pot" the stator much better. It's held up for 4 race weekends now so fingers crossed.
(I only persisted with the Chinese junk because the vendor replaced it several times for free, then I gave up and bought a supposedly better brand that turned out to be exactly the same thing. That's the one I had beefed up when new)
Next time I need one I'll probably just pay Powermaster twice as much for one that will actually work. I talked to them at PRI, they source the bits in China too but build and QC them here.
Sorry if none of this is relevant, my point only being that if you've run it at all it may simply have fallen apart inside. I would not expect a brief run w/o charging connection to hurt anything to be honest, and if it did I'd expect the regulator to fix it. (Unless maybe when replacing the regulator you converted it back to a std "two wire"??)
All to be taken with a grain of salt as I'm an ME. 8)