Was too long for the comments section. So made a post here.

I've tried it out today. 5 starts. It works and the elector counts mechanic doesn't break the game. However, you really should try to get rid of it and imperial prestige and just set the authority to a permanent +1. Because even though it doesn't break the game on a technically level it really screws up your campaign in several ways:
1. You start in a state of Civil War with all the other Imperial factions. Besides being bad by itself the game appearently blames the CW on you, since your diplomatic reliability is at "low". Screwing diplomatic efforts with your neighbours.
2. With the map being randomized, you constantly get events about provincal capitals being lost, inter-empire wars, etc etc which don't just drag you into wars. You can also loose money and imperial authority. IA at 0 or minus figures bestows some substantial penalties on growth, happyness and leadership.
Basically if you play the Empire the game mechanics still assume, that you are in charge of the Empire and penalizes you for any "lost" provinces and "internal" conflicts.

Some more minor feedback:
1. If you can tweak the RNG, I'd recommend making it have everyone start in the provincial capital of a province with at least two minor settlements to balance starting positions somewhat.
2. Have all those starting capitals provide 9 building slots on lvl 5.
I'd consider both those things much less important than getting rid of the Empire mechanics. As far as I'm concerned you don't need to bother trying to adapt it for random placement, just somehow disable it.
Anyway I'm going to continue playing with my 5th start and see how it goes. Your mod definetely is a great idea, massively boosting replay value. Enjoy having a High Elf neighbour for the first time as the Empire and go fight Greenskins and Dark Elves instead of the same old Civil War and Vampires.