This is a very interesting question. Strong parallels can be drawn between this situation and the US/USSR cold war. There are a number of differences also, so the analogy is a bit imperfect. But the cold war eventually devolved into a number of nasty proxy wars. Which is something that the Federation really doesn't want. I don't imagine anyone (on the Federation side) wants an arms race either.
And I can see both of those happening if this situation isn't resolved. It is not at all a stretch to imagine the Cardasians supplying weapons and intel to the 'freedom fighters' of the Orion syndicate to help them 'throw off the yoke of their Federation oppressors' if the Orion Union becomes a member of the Federation.
The big question is how to deal with these tactics. Ignoring it won't help. Getting into an actual shooting war should be the very last resort. Matching the Cardassian tactics will lead to recreation of the cold war, a very sub-optimal solution. Some one needs to think up a decent way to break the paradigm.
One thing that should be considered is Federation propaganda. A vehicle to disseminate the Feds view of things across the quadrant would be very useful. It might even be worth doing a joint venture with the Klingons and Romulons to create the Alpha Quadrant News Service. Lots of diplomacy work but that is one of the Federations strengths.
The Arms race is going to happen, just because neither side is going to stop designing new ships. The thing is that an Arms Race with the Cardassians is something the Federation cannot lose. Feddie R&D is AMAZING, and we're starting with a lead on both resources and industry. We're not in a position for a war to the knife. Give us 30 years and we can just curbstomp them with a doomfleet of Excelsior Refits, Ambassadors and the like. We absolutely want an arms race, because they can either play that game with us and lose, or they can not play it and become irrelevant.
Fortunately we're almost garunteed to get access to the Riala design after this event, and the Riala is cheaper and a better combatant than the Excelsior, while still being five year mission capable. We can turn out some Rialas to act as our line heavy warships, to fuck with the Cardies* and to cast aside any notion that the UFP is the Human Empire.
Depending on what all we get tech and design wise we might want to integrate Amarki stuff into the Renaissance. The Amarki Shields First warship philosphy meshes well with our schtick after all.
*Because they will be maximum butthurt at seeing Starfleet running around in capital-scale reminders of OO fuckups
Stall. Hush up. Postpone. Build our forces. We make it look like the Cardassian black ops aren't actually hurting us (and, whenever possible, that they aren't actually Cardassian black ops), and keep winning the diplomacy war in the CBZ to get more resources and allies while theirs run low.
Then, we end the Cardassian Union as a galactic power.
Eyup. The last thing you do when opposing the UFP from a peer, inferior, or modestly superior position is give them time. The Feds will tech up, build up, and technobabble up, then fuck you up. The Cardiassians are giving us time. Time to build an Excelsior/Riala/Rennesance victory fleet that we can use to roll over their fleet and dictate terms with capital ships over Cardassia Prime when we decide to go hot.
What? My vision of the UFP is that yes, they are nice, kind and diplomatic. Yes, they really would just like to get along and explore the universe together. Then you push them too far and you find out at least three of the four core members can be horrifically brutal nightmares when pushed into a corner.
