Here is a small tutorial of setting up Costar stabs.
For the plastic inserts , be sure to clean them well of any lube that might got there or in the keycap stem. It’s interesting as I had different Costars stabs and only encountered that looseness in a WASD board as well as you. At that time I used small pieces of paper to make them sit snug ( take out spacebar, insert paper+plastic insert,mount spacebar into the wire and then put in position)
You could also hunt down or ask @ for some extra inserts, they came with some JTK sets at one point and they’re also available on aliexpress type websites among the stabilizers.