Would moving a transaction from an old block to a new one allow more pruning?
This seems a lot of effort for absolutely no benefit.

In the Bitcoin pruning model you discard ALL those old blocks anyway, and JUST keep the utxo set. It doesn't matter whether a utxo is in an old block or a new block, you're still keeping it in the utxoset. Any blocks you keep around is merely for convenience and to assist other nodes that request those blocks.