I came up with a game that suits both themes:

Title: Sticky Stuff

• The player uses two buttons (or keys) to turn around, but is otherwise stationary.
• Phase 1:
  • Small objects spawn on the left, right or top.
  • They start to move towards the player.
  • The smaller objects attach to the player when they collide with it.
• Phase 2:
  • Small objects spawn on the left, right or top.
  • They start to move towards the player.
  • The objects cause damage / minus points when they hit the player.
• Each level has these 2 phases, game zooms out every now and then so that the player is effectively smaller but must collect more objects.