My preference would be genuine Cherry stabs > Costars > fake Cherry stabs, Cherry stabs being my favorite. The fit of the metal wire in the Cherry stabs make such a huge difference to the rattling of the keys, the wire on the fake Cherry stabs I had before were slightly smaller in diameter than the genuine one, which meant that no matter how much I work I put into it, there was still rattling, which really annoyed me. Genuine Cherry stabs fit a lot better and it was quite easy to fix the rattle.
IMO, only real downside with Cherry stabs is that if you mount the switches with a plate, you pretty much won't have access to the stabilizers anymore, with Costars you'll still be able to tweak it here and there and lube when necessary. One way around it is to PCB mount your switches and not use a plate, that way you'll still be able to have the benefits of a Cherry stabilizer with the convenience of Costars, although I'm aware that this affects the typing experience of the board overall and might not be for everyone.
To answer your question, No, you won't be able to swap the Costar stabilizers on the stock Filco plate unless you get a Universal TKL plate and fit it with plate mounted Cherry stabs. I can't recall if the Filco PCB has the cutouts to allow PCB mounted stabs. The mod itself used to be quite popular, but it seems that most people have moved on to smaller form factor keyboards so the demand and supply of TKL plates have decreased recently.