Here's a tip for increasing move count that really helped me:
Focus on eliminating TYPES of items. What you really want is a board that is 80% silver & gold coins - because that leads to lots of cascades & 5-matches. If your board is 15% bronze, 15% silver, 15% gold, 15% sacks, 15% chests, and 25% high-level stuff you'll probably run out of moves soon. Avoid matching the things you have a lot of, to increase your odds of getting extra turns soon.