I would absolutely try for joint custody. No matter who paid for them, you both should get to still see them. It had been done, me and my ex did it. He kept our Great Pyrenees and she came over to my house when she started getting arthitic in her hips.
She stayed with me for @ 5 months with him visting her all the time, before we had to move out of state and he just recently called me to dicuss her health, as she was getting really bad and it was time for us to let her pass. Even though he was the one with my son there physically with her, he held the phone to her ear while I could tell her goodbye.
I guess that was really off subject, sorry. Try to make a good arrangement for your furbabies and if it can't be done, I seriously recommend finding a baby for yourself. Best of luck and we are here for you.