For me, my main schismatic infighting is that "approval voting" ballots might not forward-compatible with ranked systems (IRV, Condorcet, etc.)
In other words, if we're going to go through the trouble of upgrading ballots and machines and voter-training, let's at least do so in a way that doesn't close the door on that other universe of possible schemes due to a minor technical limitation.
There's no need for voting machines, at all. As shown in Scotland, it's perfectly practical to hold an STV election with voters ranking candidates by writing numbers on their ballot papers. This can be adapted straightforwardly to approval voting, IRV, etc.
Also, Scottish voters use four different multi-winner voting systems, showing that even the problem of voter education isn't insurmountable.
In other words, if we're going to go through the trouble of upgrading ballots and machines and voter-training, let's at least do so in a way that doesn't close the door on that other universe of possible schemes due to a minor technical limitation.