The 6MB8 is a sharp pentode. The 6BM8 is a power pentode.
I guess you could say that another way, as "6MB8 is a "not-power" pentode.

"Sharp cutoff" means it is a small-signal pentode, generally for preamp or voltage amplifier use, which has characteristics you're used to. A "remote-cutoff" pentode is also sometimes called a "variable-mu" tube, and is difficult to completely cut off. They are most often used with a variable bias provided by a radio's automatic gain control (AGC) circuit, to allow weak and strong stations to sound equally loud. Some clever folks have used them in tube compressors.
A power pentode is meant for, well, power output applications.
Q2) Can a 6MB8 be used push/pull like a 6BM8 can?
You can use any tube in push-pull. The real question is what are you trying to accomplish? That, and do you happen to have a bunch of 6MB8's in hand waiting to be used? I
do happen to have a bunch of 6AU6's in hand, without a home, so my interest lies more in your original thread.
Q3) What current ma draw would there be with 270v on the plate?
Something between 0mA and infinity. I'm really not trying to be flip; for any pentode, plate voltage hardly matters, but screen voltage is essential in determining plate current.
But since we have only short-form data (I
hate short form data), let's note that max plate dissipation is 2w. So the most current we could have at 270v is 2w/270v = 7.4mA. We know from the specs given that we have either 10mA (-0.422v bias) in pentode mode with 125v on G2, and Gm is 12,000 micromhos (1.2mA/v). Gm will drop with less current, but as a first guess, we need 2.6mA less so 2.6mA/1.2 = 2.17v more bias is needed. We could then guess that 270v plate, 125v screen, and -2.6v bias will work.
Q4) Does a 47R/5w resistor sound reasonable for a shared cathode resistor?
It would be smart to plan for at least 3v of bias. According to the data sheet, the ratio of plate to screen current is about 3.6:1. For 7.4mA of plate current, screen current should be about 2mA. Cathode current is then 9.4mA, so the cathode bias resistor will be about 3v/9.4mA = 320 ohms; 330 should be close enough. For sharing between two tubes, tend to the high side with a 180 ohm resistor. 18.8mA * 180 ohms = 3.38v * .0188A -> 0.06w, so a 1w resistor should be plenty.
You'll probably have a separate power supply node for the screen supply. Take these numbers as an example to work based on that node's voltage. We have 270v, and need 125v on the screen (if we had more complete data, or breadboard testing, we could use other screen voltages). We know the screen will pass about 2mA; 145v/2mA = 72k, 75k is close enough. You'll need a bypass cap to ground from the screen pin, as you see in preamp pentodes. A .1uF cap is -3dB down at F = 1/(2*pi*.0000001F*75k) = ~21Hz. A 1uF cap would be a solid bypass and help keep hum out of the screen.
Will continue separately with possible good OT primary impedance.