There's a culture decay rate which controls how quickly culture spread tapers off per planet; adding a racial trait ("level zero" or starting value has the bonuses, e.g. you don't need to research it to get the bonuses; see the Enhanced 4X mod for this, though I'm sure there are other possible implementations) and culture spread rate increases the rate at which it, well, spreads.  Note that the culture resistance IIRC only affects how slowly the enemy's culture penetrates; so if I'm not mistaken, given enough time, without any friendly culture spread an enemy culture would still, slowly, fill the well.

You could also buff their cap. ship culture repel rate, which would dispel hostile culture in neutral/friendly grav wells; in effect serving as a mobile planet in this regard.  This might allow them to, say, bomb an enemy planet to rubble (make them strong at bombing, perhaps, or give them a Kostura type workaround?) then their cap. ships would automatically start cleansing the enemy's culture.

I'd give them an insanely high culture resist trait, and a massive penalty to culture decay rate as a minimum.  I'd also recommend that you buff their cap. ship culture effect and ensure that they can get culture up and running relatively easily, perhaps even through trade ships or something unorthodox/out there if possible.

Alternatively, if you're willing to mod the global constants, you could allow cap. ship culture repulsion to work in hostile gravity wells as well (this would benefit the other races, too) so a massive culture repellant bonus would allow an assault force (or even one "passing through") to start erasing culture even without exterminating the planet... i.e. if the player hasn't placed culture centers on most worlds, then I'd suspect the culture repulsion would make a mark even in a hostile grav well.  It could essentially make a player consider building more culture centers to prevent raiders from simply erasing it all.