I wonder if I'm confused.

Could one register a normally certified if small aircraft (say an Ercoupe) to LSA and then convert it to an E-LSA and then do one's own maintenance and modifications to it? I assume there is some rule somewhere stopping this but cannot find it.

There is an S-LSA to E-LSA path, I have a friend who did that on a Zodiac 601xl. He got a repairman certificate and can do his own maintenance.

No idea if there is a certified to E-LSA path. I have heard of many certified aircraft converted to experimental for STC testing, but the limits are so painful people put them back to certified as soon as flight test is over.

short answer, no

but we can dream of something akin to the Canadian owner-maintenance category. I think it will happen eventually