Let's say I'm using The Bug. I am on the last click of the Beetle dial and I take 4 damage, after giving it 1 damage that dial KO's. Does the damage carry over to another dial or is that the end of the damage?

That's the end of the damage. The dial fully absorbs it.

There is a clarification in the Player's Guide that damage does not carry over across multiple dials.

I really wish they would redesign the peanut dials to have two dials on them. Also, they are hard to turn as the mould for them is not making as deep of a "H" on the bottom.