And on top of that, the meta issue is that whatever you can do to destroy US cities, they can do back to you sevenfold or more. Oh, you have gas missiles? We have missiles, and four-engine bombers based out of Ontario and Michigan and Nebraska, (out of range of CSSA counterstrikes, not because they can't reach it, but because the attrition over those air defenses would be
horrendous), gas weapons of their own (*Lewisite, phosgene, and sulfur mustard work fine if you just
use enough), probably early nuclear weapons, superiority in conventional and rocket artillery, you name it. They can make it rain, none of your airbases or missile sites are out of range of anything they want to drop on you, and you have a much smaller population.
So what's a winning strategy? Make every fucking inch of ground a hellish nightmare to take and hold, a Saarland writ large. Mix in to your jumping mines early *claymores, gas mines, flame mines, and miles and miles of dragon's teeth and ditches. Build a fleet of turretless tank destroyers that can fight buttoned up on a chemical battlefield. Chemical shells for everything from light mortars to your largest field pieces. You don't have to make it impossible to invade; you just have to make it political suicide for whatever US president
tries. If the butcher's bill is high enough, that's an effective deterrent.
(I have to say I'm skeptical of any CSSA superweapon that relies on scientific and technical prowess. I could see them having good applied science, but I can't see it being a world leader in any of the fields where wunderwaffen could sprout in this time period. Something like the S-mine could be highly effective at the desired task of making invasion too expensive, especially if it's backed by a comprehensive defense strategy and a line of secret super-gasses.)
EDIT:
If you haven't checked out Francis Spufford's
Red Plenty, this is entering a plausible era for the CSSA to be looking like a paradise about to come. The old, corrupt, pellagra-ridden CSA is dead and buried; this is the gleaming steel future of central planning and mass production for a newly educated and politically conscious Confederate proletariat (we'll conveniently ignore that it's an order or two of magnitude poorer than OTL's American South in the same period by necessity; by the standards of the Confederate citizen of TTL it's prosperous), where everything from food to housing to education is available cheaply and distributed equally.
In the ATL 1948 the CSSA's system will appear, insofar as most outsiders can see, to be working, maybe even outperforming capitalism in some areas. Aggressive agricultural industrialization might be one of them; dietary science and public fitness might be another. Cheap, wholesome foodstuffs to replace the poor old Confederate diet of 'white foods'; sports clubs, exercise groups and spa-resorts designed to keep workers at peak efficiency, scientific dietary advice disseminated through Party periodicals and in Party-approved and assembled cookbooks like this old Soviet one:
https://www.amazon.com/Book-Tasty-Healthy-Food-Cookbook/dp/0615691358 and goodies like the *Mikoyan cutlet and hematogen bars (which you wouldn't believe if I made it up).
(I'm carefully trying not to think about some of the atrocities that could be visited upon the artisanal French countryside foods I love so much OTL in TTL's European Syndicate.)