Chief O'Brien called them the Border Wars, did he not? It's not a huge point, but perhaps it sounds less grandiose than "Federation-Cardassian Wars", reflecting that it was a series of skirmishes rather than a full-blown total war.
Good way of explaining the higher numbered Excelsiors though, and a nice way to end on Sulu. But I've got to say, these TOS characters were practically indestructible! Spock, Bones and Scotty are known to be at large in the 24th century, and if you go by the "non-canon" materials, Uhura's the chief of Starfleet intelligence, and Jim Kirk himself is kicking ass like a 25 year old.
Hopefully Chekov died of a heart attack aged 59 to balance things out!