So I'm planning to go and play this game again, and since I'm a perfectionist I'd like to know about possible miss-able items that don't even spawn back in a New Game+.
Are there any such items, or does a New Game+ include the exactly same data as a normal New Game?
There is nothing in a New Game that is not available in a New Game +.
The New Game + contains the same data as a New Game. The only difference between the two is what you carry over from a New Game to a New Game +.
There are so many items that do not carry over (i.e. key items, Lv7 Techs) onto a NGP and must be reclaimed each playthrough, but stat gains are randomized so your characters will never reach their full potential (theoretically). And, there are items that simply cannot coexist without gamesharks, like the Sea Swallow/Mastermune or Prop Sword/Hero's Sword. Careful not to end up in a medical ward if y'can't play without perfectionist tendencies...
There is one event that is in a way missable in New Game Plus: Spekkio. His levels increase as yours do, and you get an item set the first time you beat his various forms. Since you keep your levels, if you miss one of his forms, you can't face him at that form ever again, even in New Game Plus. Of course, the items he gives are all common items and Tabs, but I thought I should mention it anyway.