This is a really good topic! Good lord, I forgot about Squidward stuck in a freezer for 2,000 years.
Because Squidward went back to his present day at the end of the episode, he was free to enjoy life again. Somehow this other Squidward who was frozen (we'll call him Frozen Squid and the other Present Squid) never appeared in other episodes in the freezer. Probably because faulty continuing references, that's the best I can come up with.
Remember in Back to the Past? The Mermaid Man and Barnacle Boy who went back in time eventually DIED because SB & Pat left them there. That's seriously one of the more morbid SB stories out there! (I'm surprised S̶B̶ was able to forgive himself after that though, being the big fan of the guy he is.) Nevertheless, both MM & BBs from both time eras were clearly able to live together and have no time paradox. Plus remember all those S̶B̶ and Pats at the end who came together from different periods of time? So time paradox is definitely not the issue here.
I think the thing is, the Krusty Krab Crew could have buried Frozen Squid in a cemetery. Similar to the episode Nasty Patty. Even though he could have been easily thawed out, it doesn't make sense to have two of Squidward right? Because two of the same people can't have different mines and be a clone of each other or can they because of human/fish rights right?!
Okay bad theory, but it's still a good guess. My last idea is somehow the Frozen Squid just "poofed" away unexplained. This makes no sense as I said earlier that time paradox are not likely to happen. That and even though it hates me to say this and I feel like it's the easy way out to the question.... it's a continuing error or as everyone says "it's just a cartoon".

With all the times the show has not explained things throughly enough, this makes sense. It's just one of those things that as hard as you try, you're not likely to find an answer. (Or at least me. Especially with my thread about how a visit to the medieval ages made it possible for the KP secret formula to be both a family and Krabs original recipe.)
And let's talk about the whole thing about jellyfishing. Clearly S̶B̶ and Pat can be seen doing so in past episodes like of course, Jellyfishing. :P The thing that gets me with time traveling is this... does time travel work where if you live in the past and your future self did altered the past (or present your time) but have YET to do it in your time, does it effect you? Like for example....
Because someone goes back in the past and changes it, do they alter past events with friends? So when we were watching the episode Jellyfishing, was it considered the invention of Squidward yet? (And if S̶B̶ and Patrick know, you think that Squidward would be flooded by fan boys from various jellyfishing expos all the time. Maybe he is.) I don't think it was his invention yet, because Squidward hadn't went in the past and change jellyfishing yet.