First of all, let me congratulate you on your introspection. This type of behavior is pretty rare in the game (and the forums).
Anyone reading this post will be impressed with your politeness and class.
Ask yourself the following question: Will these alliances be happy to see you arrive based strictly on your: Donation , trophies, King level?
If you have a high donation level, they will be all smiles to see you come and no one will ask when your invite was sent.
In most alliances several people send invites and you never really know who sent what, so they will not know the invite was sent months ago. If they do track when an invite was sent (I used to do it months ago because I sent out so many (read 100s) and wanted to avoid spamming the same players too much) I would not accept players that used old invites. Not because they were slow to respond but because we grew so fast that the requirements changed from week to week.
Hope this helps!