Apart from the tutorial first level, has anyone unlocked all the locked pieces and cleared the board yet?
Yes, a couple of times.
It seems that if you want to clear the board then it's all about looking ahead at which element you need to (or will) transform into next (2 pieces, 3 pieces, key head, key body, etc) and maybe using that new shape to clear similar-shaped, locked pieces. They soon go but then you use them up and the next spawned piece may not be usable straight away.
If you want to collect keys for the chests though, then it's best to convert fully keyed-up pieces rather than unlock similar ones with them.
Also keep an eye on what each piece will give you as a reward if you merge with it, some are better than others.
Always try and keep at least one each of the key head and body available, don't leave yourself with all heads, for example.
This is where the strategies and choices come in and they depend on how you want to play.