This is only a working theory I have come up with reading this thread, so take it with a grain of salt.
One way to help solve the problem is to place the Cardassian Union on the other side of some other species that had caused problems for the Federation prior to the TNG time frame (yes I'm thinking in basic 2-D terms). During the TOS time frame the Federation was dealing with the existence of the Gorn, Metron and the First Federation, by the time of the Movies the First Federation seemed to have been resolved, the Gorn/Metron later still. So the Federation now continues exploring out in the same direction next they find the Tzenkethi and have a minor war with them, hints of the existence of the Cardassian Union begin to emerge, the Cardassians start to hear about the war between the Tzenkethi and some new Government called 'The United Federation of Planets', colored with Tzenkethi propaganda. Once the Tzenkethi War is dealt with the Federation explores some more, only to find the paranoid Cardassian Union, by this point were into the mid 24th century and haven't really gone that far away from the core of Federation space. Now by the TNG era, the Federation has had a war with the Cardassian Union, however we don't know the exact dates or full outcome. Only a few years later, DS9 era, the Cardassian Union starts another war with the Federation this time with the help of the Dominion, Starfleet hasn't tried to explore around them yet.
One other to look at this is the difference in distance you get while traveling in the mountains. The distance from my home to that of my parents by road is about 60 miles, due to a 14,100 ft tall chunk of granite right between us, "As a Crow Flies" my parents house is only about 15-20 away however. So if I could just go through the granite the trip would be a lot shorter. The Gorn/First Federation/Tzenkethi are the granite mountains blocking the direct path. By the time of DS9 all but the Tzenkethi have been turned in to mild hills, allowing for traffic to pass through relatively unhindered.
Any way, just trying to come up with the simplest explanation for a complex problem. Your opinions my vary.
Phoenix...
"I'm not saying there should be capital punishment for stupidity,
but maybe we should just remove all the safety lables and let nature take it's course"
"A Place For Everything & Nothing In It's Place"