Electromagnetic 7-segment flip display: H-Bridge alternatives?
You have 28 bipolar electromagnets so it's difficult to use a matrix arrangement unless they will reliably not flip with 1/2 voltage. Diode isolation won't work. I suppose you could consider putting a bipolar TVS in series with each coil, and boosting the drive voltage (already pretty high for the driver though). Targeted coil sees +/-(Vs - Vz), non-targeted coils see +/-(Vs - Vz)/2.

For that to work you would need drivers (quantity more than \$2\sqrt{28}\$ , eg. 5 x 6 matrix, total 11, that can be driven high, low or high-Z so still 22 control lines at the driver level). 

If they won't do that you actually need to control 56 logic states at the driver inputs. So maybe you could flip one at a time and common one of them up (29 wires), but I would think a shift-register would be superior. 74HC595 x 7 pieces. Needs 3 GPIO (or fewer, with tricks) from the RPi. You can use RS-485 with terminated twisted pairs or RS-232 (low speed) drivers/receivers for the lines if you want the display remote. CAT-5 or similar cable could be used.