Dude, you are not helping your case. It was established in DS9 that there was a Cardassian of note (not some random Cardie that ventured away from his home planet) on Vulcan (Ezri seemed to talk as if it wasn't unusual for a Cardie to show up on one of the Federation's core worlds at the time), Organians mentioning them in Enterprise, and that drink in the movie. The destruction of the Kelvin wouldn't have made contact with Cardies sooner.Is there any cannon evidence the Cardies did do anything in that time frame? The Klingons were menetioned in TOS , even if they only showed up in 7 episodes, people still knew they existed, they made their presence known, now and again. You really can't say that for the Cardies in TOS, can you?
Plus if the Cardies could occupy Bajor and fight a war with the federation in the era right before TNG, it shows they can do two things at once. So clearly the Cardassian Union could have fought a war elsewhere and still have had some ships to protect their border with the Federation in the TOS era. Frankly you have no cannon evidence that the Cardies were involved in a war with another species back then.
That's three pieces of canon evidence that supports that there was at least some knowledge of the Cardassian civilization during the time of TOS.
BTW, it was established that for a good part of the 24th Century, there was no contact between the Federation and the Romulans prior to TNG's Neutral Zone. That means if we had a Trek series between mid-2310s and 2364, we could have a whole set of episodes without a mention of Romulans. Should a viewer who have never seen TOS, Enterprise and the recent movie assume The Federation weren't aware of the Romulans prior to 2364?
Except when have the Cardassians ever engaged in a isolationist policy like Romulans did, the Romulans at least have history of isolation, something the Cardies do not have. So why again where the Cardies not active in the TOS era?
Those examples seem more like continuity errors then anything else.
Frankly at this point the only way you explain the lack of Cardie involvement in the TOS era, is due to the fact that the military coup didn't happen yet and the Cardies were not an expansionist society yet, which means Alpha Memory was wrong.
Denobulans weren't mentioned during TOS either.
There is no evidence of Cardassian Union's state during the 23rd Century either way. One cannot truly determine whether the Federation were aware of them or not. Cardassians do not need to have been isolationists in order to have no conflict with the Federation during TOS. They may have more pressing matters elsewhere. They most likey have neighborhooding races besides the ones we are aware of, on the opposite side of Cardie Territory from UFP.