You only need chain of custody if the Bill of Sale doesnt match the Registration, then you need BOS chain to go back to who the FAA knows owns it.
I guess you still havent gotten your Varieze debacle fixed as you still think it cant be done.
FWIW. I own one airplane that had the Airworthiness paper "missing". Non event, FAA sent a new one.
My other airplane I just bought, was a de-registered from the original builder, next owners had the DAR come inspect and give a new plane airworthiness and paperwork. Sounded pretty easy.
Hope you get yours sorted out some day...