Joey,
First of all at 200V your max mu will only be at the 17+ to <18 gain region.
Second, Current determines output impedance as you change the slope of the (Imax-Imin) - (Emax-Emin) load line.
Third, tube musicality and it applies to all tubes for that matter has inherent frequency response within their class A envelope, this musicality changes with the plate construction, reactance of the electrodes and the material used in the plate. Current may have influence but very minimal that is totally inaudible. So a Sylvania will sound different from a Tung Sol from an RCA from a Raytheon. 12AU7A will also differ to its electrical equivalents like 5814 and 5963 made by different manufacturers.
Fourth, changing the current will change the output impedance and will mismatch your output network, which in the case of the 12AU7 is an RC Coupled network. This will cause distortion either constructive or destructive, thus eventually sound coloration.
Fifth, Sound coloration is driven by the RC values and the Q of the reactive values (Q fator is a description of the sharpness in frequency response)
So to conclude, if you change the current of your 12AU7, it reacts to new type of coloration to your output but will be truly attributed to your output RC network, thus tweaks go to that direction or roll the tube you use.
JM