Bill G4WJS  (lots of Bills here....)
"If I understand correctly, you are saying that while using one of the WSJT-X "Settings->Radio->Split Operating" options you selected a Tx audio offset, say 1000 Hz, on a VFO dial frequency, say 14,074 kHz, and observed the transmitted signal was *not* at 14,075 kHz (lowest tone frequency)"
Yes, this is exactly what I am saying.  And as I pointed out before, this also happened to NU4E during the contest so the problem is not unique to me.  We discussed the problem on the phone during the contest.  We both understand how the "split" operation normally functions.
I was not able to clear this problem by rebooting the computer. Probably I can reproduce this again.  First chance I get I will bring up he SO2R operating conditions and see (using 1000 Hz TX audio selection on the waterfall} exactly what the split VFO is reading while transmitting and then measure the frequency it is actually transmitting.  When the problem is present, both the FT signal and the tune button have the same problem.
"Why do you need to use anything other than "Settings->Radio->Split Operating->None" when you are using an all digital audio chain, and a rig with variable Tx and Rx bandwidth?"
As Frode previously pointed out: The purpose of those two settings (Split - Fake It) is to make sure that the FT8/FT4 audio signal stays between 1500 and 2000 Hz (to avoid the risk of intermodulation in the audio passband). If you select an audio TX frequency (the red "goalpost" in the waterfall window) between 1000 and 1499 Hz, say 1200 Hz, you would expect your signal to be transmitted on e.g. 14,075.2 kHz. To transmit an audio signal in the 1500-2000 Hz sweetspot, the USB "carrier" or dial frequency is therefore moved down from e.g. 14,074  to 14,073.5 kHz. Your audio signal will be 1700 Hz, right in the 1500-2000 Hz sweetspot. Your signal will be transmitted on 14,075.2 kHz, which is the sum of  14,073.5 kHz + 1700 Hz.
WSJT-X User Guide as has this info: " Either method will result in a cleaner transmitted signal, by keeping the Tx audio always in the range 1500 to 2000 Hz so that audio harmonics cannot pass through the Tx sideband filter. "
I will be back later with the info you want, Bill.   I *DO* appreciate you responding.
Bill N4iQ