I doubt there's a cut and dried answer for you, Simon, like 'Use a new move 40% of the time." or whatever.
The game is limited by the moves you have available. (That's not a bad thing, it just is.) Until you feel comfortable using the whole array of moves at your disposal, you don't have as many options to rock the game with. Once you get a handle on the full array of moves, you may find that your game rocks just fine using a smaller selection - or that the game rocks that much harder with additional moves.
On the other hand, you don't want the game to suck while you practice your new moves. And unfortunately, I can't think of a way to 'woodshed' MC skills.
My thought would be to limit the amount of new material you're trying to get a handle on and break it into more easily managed bits. You might try restricting yourself to just one or two Threat Types to start, or maybe limit the number of moves for a Threat type, and add more as you get the hang of it.
Like rather than putting all five threat types into play, limit yourself to just Brutes and Afflictions, or whatever, until you get those down.
Or you could just use, I dunno, the first three moves available to the Threat, like Warlords would have these to start:
• Outflank someone, corner someone, encircle someone.
• Attack someone suddenly, directly, and very hard.
• Attack someone cautiously, holding reserves..
..but they wouldn't initially have access to the 'offer to negotiate' or try to 'buy out someone's allies' moves.
This isn't all that different from the way PCs get new moves as play progresses. The advancement is informal, so if you got to a point in play where you go, "The Warlord should totally make a show of force here!" then have 'em do so. But by limiting your choices, you're not trying to take in the entire list of moves at once.