With the long term attachment you have to them I would suggest that you spring for the thirty dollars apiece it would cost you to have them chromosome sexed.
If they are a pair you will easily find a home for them where they can be together for the rest of their natural lives. If the tests reveal that they are of the same sex then things might be more difficult, but no more so than you are facing now. If you can find someone willing to adopt two adult red loreds you must be very careful about them. As you well know they are not the easiest pets to have.
I love red loreds. Ive known many of nearly all the subspecies available in captivity. But as mature, bonded birds they are not easy pets. Actually no amazon is an easy pet. You have to love them.
Just my opinion.