I wonder if you searched if you could find someone else with a different bloodline that got nekid chickens and get those together to save the naked genes and still introduce new blood
If the nakedness is caused by a single gene, then it's easy enough to add new blood.
Cross a naked chicken to two different unrelated chickens, then breed the offspring together to get about 1/4 naked offspring (but now with about 50% new blood.) This can be repeated as often as you need to or want to.
If the nakedness is caused by a combination of multiple genes, then it's a bit harder to add new blood and still keep the naked trait, but a single gene does seem the most likely explanation.