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Combat is fun, and it's nice to control! I found myself spending almost the entire time in the monster dimension, since the consequences of doing so felt pretty negligible (for me at least). I think you could add more unique aspects to each dimension to incentivize the player to balance their time in each.

 For example, you could have enemies move faster than you in the monster dimension but not in the normal dimension, and add an enemy type that chases you down. So if there's a lot of them chasing you at once you might need to switch to the normal dimension until you've dealt with them or gained some distance. 

That's just one of many things you could implement, the combat in 2 dimensions concept has lots of potential I think 

(+1)

Excellent ideas, I had some ideas for how to implement better incentives to swap, but just ran out of time, but I love what you've suggested. If you haven't, give the endless mode a try, that (should) make staying in a little more dangerous as the waves go on. : )