For the split cards, that wouldn't work for copies. Copies are actually, I believe, one of the main things that stop the cards from being made. I'm not 100% aware of every reason they won't work. If I was, I might be able to come up with something that's at least close enough for people to enjoy using them. At the moment, I know that a couple of split cards exist as two separate cards entirely.
For the upkeep, I'm not sure why the manager wouldn't be working except that maybe you didn't add the cards to the manager's function. The UTM works like this: each card that may need upkeep time management creates the manager. During each player's upkeep, the UTM checks the battlefield, hand, and graveyard for any card and compares those cards to the cards in its function file. The function file contains information such as cardname, zone, and any other requirements the card needs to function. If everything it needs to function is met (the card exists in the proper zone, the player can afford the mana cost if there is one, and various things like that), then the UTM creates a single delay (even if it finds several cards that need an upkeep time window). If you didn't add the card to the function, then it won't recognize that as a card that needs upkeep time.
As for
Braid of Fire, it should be working. I'm not sure why it isn't. I'll look into it when I get time, but I don't know when that will be.