What do I do if mandatory actions will inherently take a very long time to resolve? (Splinter Twin + Tyrant of Discord example)
If such situation as described by you really applies, only the judge can help in this situation. 

I have various examples how a judge handled alike situation, but most of them had one thing in common: It ended in a draw.

The examples that didn't, had in common that the player determined a way to shorten the "choose randomly" process. Here it becomes quite tricky.

In the end the judge with the right authority does have the last word on this and it cannot be generally determined for all tournaments. This is an example of a gap in between the rules that propably needs some fixing for a fair ruling.