Forgive me as I am new to quilting, but what about somehow attaching a small strip of the original pillowcase fabric underneath the lacey edges so that the "block" still shows the embroidery and the lacy part with a bit of white below the lace? I dunno if that would work at all but it was just a thought. I'm thinking your blocks might not all have the embroidered piece in the center necessarily, but you would still be showing your lace edges like you want. Just an idea.
Good luck with the project... the pillowcases are simply beautiful and I applaud you for wanting to create a new heirloom to showcase them.
Candace