IMO, if you've had them for a long period of time and you are the one providing for them AND he chose to leave them than that should make them yours.I don't know the reason he left them but if he just deserted them than he has no right to them. Maybe I'm wrong, but that is how I feel about your situation. And how I would be if I were in that position, if he didn't care enough to take them with him then he doesn't care enough for them now.
Why does he want to GIVE them away?? It sounds to me like they have a home were they are cared for and loved very much.
I've had 3 cages here before so I can see where you are coming from on the amount of time you can give each one and how hard it can be sometimes.I don't doubt your love for them, I loved all of mine as if they were my kids.The best advice I can give is to follow your heart, it will usually steer you in the right direction. You will definetly be in my prayers.