Have you checked what mooshimeter sees there in burst mode?
I’m quite sure that 4 (or 8) kHz sampling can’t basically even see that 1kHz signal, or at least datapoints would be so random, that it is impossible to guess that there is sinewave or anything else..
Pure sinewave at bit higher voltage might be possible to nearly 1kHz, but i have no idea what mooshimeter would show then.. Damn, i actually did play with amplifier and some android “signal generator”, but cant remember what happened :D .. Somehow that 1kHz seemed familiar and i think that at least in burst mode it was (human) readable.
Did you use voltage terminal for your measurements, or “ohm”-terminal, that does “precision” voltages to +/- 1,2 volts?