I love the title of your post!
The Mu of a tube is also referred to as the voltage amplification factor (this is more descriptive). For instance, the 12AU7 in the Crack lists a Mu of 17. So under ideal conditions, if you put 1V of signal into the input of the 12AU7, you'll get 17V out. This is 24dB of gain.
If you adjusted the circuit to use a 12AX7 (it won't plug and play correctly), then you will get 100V out from 1V, which is 40dB. This leads to the situation where the first 5-10 degrees of volume control rotation control the listenable range of the amplifier.
You also mentioned current and its relationship to Mu. There's a little bit of missing piece in here, which is Transconductance. Transconductance is like Mu, but in terms of current. The three of these are related by the formula Mu=Gm*Rp. So to get gain of ~50, you can have pretty low transconductance and high plate resistance (12AY7) or high transconductance and low plate resistance (6C45PI).
So, in summary, the selection of the driver tube is primarily motivated to keep the gain under control. Consequently, the alternate tube types used are along the lines of 6SN7's, ECC99's, 12BH7's, and 5687's.
If you picked up something like the Paramounts or Stereomour, selection of the driver tube will become a bit more dependent on the Rp variable as well.
-PB