This is a very nice idea.
The problem is the following: We can not bring blocks to the far left or the far right side, because we can only pull. This results in there always being a "pile" of blocks in the middle of the field and empty holes at the sides, forcing us to destroy that pile. If there were a method to push blocks as well, this would not be an issue. My recommendation therefore is the following:
1.) Keep the "pull" tongue on "C" as it is, exept for also letting us pull blocks that have already landed. I know that the original tetris idea is to not let us move blocks that are landed, but by destroying blocks under landed blocks they become moveable again anyways until they land again.
2.) Add a "push" tongue on "V", it will push blocks away or crack/destroy them if they are jammed. (Maybe shape it like a fist, maybe make it a bit shorter than the "pull" tongue, maybe give it a longer animation, maybe give it limited/refilling uses, maybe ...)
3.) Add a "movement" tongue on "B" that works like the grappling beam in Super Metroid or the hookshot in Enviromental Station Alpha. This will add the required mobility we need to maneuver efficiently.
Good start, dont give up!