How to power a big high voltage 7-segment array with minimum parts, without frying my wimpy power supply?
Since you are already multiplexing your digits, you should have no problem with current drain. 7 segments times 50 mA is only 350 mA. And the number of switches required is simple: 8 segments plus 8 digits equals 16 switches. However, the digit switches must be of the opposite polarity from the segment switches unless you are willing to learn how to make high-side drivers. 

For instance, let's say your display is common-anode. Then you would want 8 PNP (for BJTs) or 8 p-type (for MOSFETs) for the digit anodes, and 8 NPN or n-type for the segments.