You hear what you hear, if that's nuts then we're all looney. I would contact the speaker manufacturer on the second question, they can give you the correct answer. You will get some responses to your post here telling you it's okay and others telling you it's not okay and then it usually(not always) turns into a pissing contest between posters. Sad but true.
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Actually, I think there is a better consensus (though far from a perfect consensus) on this question than on many other issues in audio. The consensus being to go with what sounds best. And no, you won't hurt anything either way.
Re question one, there are many reasons why it is possible, led by the fact that the speaker probably deviates considerably from 6 ohms at many frequencies. Also, the higher output impedance of the amplifier on the 8 ohm tap will accentuate the effects of the variations in the speaker's impedance vs. frequency curve, and will also result in a lower damping factor and therefore lessened bass control. Also, the plate circuits of the amplifier's output tubes will see differing load impedances depending on which taps the speakers are connected to, with resultant effects that will vary depending on the amplifier design.
The bottom line is that the amplifier-speaker interface is complex, and both components differ from idealized models in many ways, meaning that the only way to reliably predict what is best for specific components is to listen, and perhaps to compare notes with others who have used the same or similar components.
Al's response covers almost all of the substance on the impact of different taps, save one issue:
Some amps have "good" sounding taps and "bad" sounding taps, regardless of the speaker load presented them. Variation in output transformer design and manufacture can be material, varying from model to model and even between examples of a given model. From your post ("tinny" treble), I wouldn't be surprised if the issue turned out to be sub par 8 ohm taps on the Ming Da.
BTW, the issue of manufacturing variability extends beyond taps (though it's less commonly a real problem, IME). If you test enough pre-amps, you'll eventually encounter it. Two different line level inputs on the same pre should be identical sounding, but -sometimes- this isn't the case. IME, the "sometimes" is much more frequent on output taps than on line inputs.
So, a number of folks have suggested that if the speaker impedance curve drops below 4 ohms at places, and I am using the 4 ohm taps, it risks overstrain on the amp and amplifier damage. Is that an unrealistic concern, even if I am listening in the triode or Class A mode where output power is about 40 wt/channel? (I obviously can't find an impedance curve for these speakers)
Contrary to what you may have read or heard, I would expect (with one irrelevant exception described below) that for any given speaker there would be LESS strain on the amp using the 4 ohm tap than using that same speaker on the 8 ohm tap. Although as I and others have said, it is extremely unlikely that you would have a problem either way.
The 4 ohm tap puts out lower voltage than the 8 ohm tap, which would result in less current flowing into a given load impedance. Also, the load impedance seen in the plate circuits of the output tubes would be higher (again meaning less current flow) if the speakers are connected to the 4 ohm taps rather than the 8 ohm taps (since the load impedance seen on the primary side of the output transformer is equal to the load on the secondary side multiplied by the square of the xfmr turns ratio, the stepdown ratio to the 4 ohm taps being greater than the stepdown ratio to the 8 ohm taps).
The irrelevant exception I alluded to would be if the speaker impedance at some frequencies dropped down to outlandishly low values, say 1 ohm or so. In that case the output impedance of the amplifier would become a significant determinant, and perhaps the major determinant, of how much current would flow from the amplifier. And since that output impedance is lower on the 4 ohm taps than on the 8 ohm taps, greater current might flow from the 4 ohm taps in that situation. However, the only speakers that I am aware of that have impedance curves dropping down that low are certain planar speakers like the 1980's Apogees. I am not aware of any box speakers that do that, and certainly none that are rated at 6 ohms nominally.
I suspect that those who may have asserted the contrary are misled by the fact that a lower impedance speaker, or a speaker that drops down to low impedances at some frequencies, which would typically be connected to the 4 ohm taps, represents a more difficult load than a higher impedance speaker, which would typically be connected to the 8 ohm taps. But here the speaker is not a variable -- we are talking about connecting the same speaker to one tap or the other.
Finally, take a look at the video Pacific Valve has about your amp: http://www.pacificvalve.us/MDMC34AB.html. Fwiw, it is described as an amp that "loves difficult loads."
Not to worry!
The 4 ohm tap puts out lower voltage than the 8 ohm tap, which would result in less current flowing into a given load impedance.
I should have added to this statement that you will tend to turn up the volume control a bit to compensate, i.e., to obtain equal volume regardless of which tap you are connected to. However, that does not change the rest of what I said above unless you were to clip the amplifier to a significant degree, which would be plainly evident as distortion.