Why would either Texas, Louisiana or Oklahoma see oil wealth go to Richmond? It's not like their oil wealth really go to DC in OTL. And here we have a states rights anti tax federal government.
It depends on the sort of shape CSA would be mentally. I can see an East German-lite bent, minus the ideology, a siege mentality with a bigger neighbor that speaks your language and can easily infiltrate you with some portion of wealth sent for defense against the hated bigger foe. It's not likely, but it's a possibility. CSA could have gone a million different ways, depending on external conditions.
It's worth noting that we, in the year 2016 think of nuclear terrorism, but rarely think of thermonuclear wars between superstates. In 1986... And that's just 30 years. The neuroses of nations are not always driven by their domestic agenda and ideology.