As he and me said earlier: this is only damping the resonances from the underlengths. It is nevertheless important to do that is there is no moving/suspended tailpiece.
If you want to experiment with foam, use dense foam. But the problem is that for the lower partials you need to mount the foam not too close to the bridge and then you get buzzing from the strings which hammer against the foam.
You might ask
@Francois Blais for advice. He has used Jargars on his EUB for less sustain and maybe he can give you better first hand advice.
For the „tone filter“, search for that name on Talkbass. There has been a picture how to use them too.
Basically a disk of rubber, about 2 to 2.5 cm in diameter, 1 to 2 mm thick, with a hole in the middle, about 5 mm in diameter. (When the string is under tension, it must lay in the groove at the bridge as normal. No rubber between bridge groove and string. )
Put it under the string at the bridge so that you can see the bridge string slot through the hole and tighten the string. The disk will bend and press against the string from the underside on both sides of the bridge.
This will kill brightness and is meant to be used for a new string until it calms down after a few weeks.
Thicker rubber disks will press more against the string and damp more.
You might get some valve seals in that form to experiment with. The hole might be a bit too small, but there are tools for making holes in leather that can be used for that. Or get some rubber rests somewhere and cut them yourself.
Or you can contact Pirastro asking for some tone filters for double bass strings. If you don’t ask for too many of them they might send them without charging anything.