Of course there’s a simple answer to all this, as there often is.
Make the PL a Sunday league, save for any teams playing in the CL the following Tuesday. They could play 1230 and 1730 on the Saturday (or even 2000 on the Friday) and thus leave Saturday free for the rest of the pyramid. It’s then not a huge stretch to have all the PL games available for broadcasting. It’d also mean far less fannying around with date and kick off changes. Everyone’s a winner…..
EDIT. Of course, it would need a fundamental shift in Sunday public transport arrangements!