would I be correct in thinking that these dbm values, as well as the
ones you referred to, mean decibels above a milliwatt into 600 ohms?
Yes. However:
Generally speaking a problem is likeliest to arise in cases in which the
amp is high powered (and most or all of its power capability is
actually required by the user, at least occasionally), since there tends
to be a **loose** correlation between the power capability of various
amplifiers and the input voltages required to drive them to full power.
Usually higher powered amps have more gain. This is because they are often used on lower efficiency loudspeakers, and the gain is need both to make use of the preamp signal and also to make the voltage swing needed to drive the output devices. The result is that with a pro audio tape machine usually has more than enough drive to work in most situations.
Depending on the machine, if its output is not loaded at 600 ohms, it may well make more voltage. At any rate I've run tape machines directly into power amps many times with no worries. The exception as you correctly point out is that older consumer decks often do have lower outputs, the standard for many cassette machines was 1 volt. But I think we aren't talking about consumer machines here.
Next step could be asking Ralph to custom make playback head tube preamp
or maybe playback head/phono stage unit, and match it precisely to his
amps, and match the amps to speakers. Now that would be high end.
:) We offer tape EQ in our MP-1 and MP-3 preamps and they work pretty well with our amps...