Hi. I strongly recommend you to go for gel purification as you will solve the undigested plasmid problem, eliminate the salt buffers of restriction and dephosporylation reactions. Surely you will lose a lot of DNA during the purification, but just star your experiments with 3-4 ug.

You could instead design primers to amplify the region of the plasmid you want to cut, digest your reaction with DpnI to destroy your template, and then cut your PCR product with the restriction enzymes you need for cloning moving forward. That would certainly improve the yield of your backbone.

If you instead need to do it this way, a trick I found with improving the yields from my gel purifications involved putting my gel slice in the -80C for 2-3 hours and then during the DNA elution use elution buffer pre-warmed to 50C. Both seems to help.

From your question it was not clear if you wanted to isolate the cut plasmid or the uncut plasmid. If you want the uncut plasmid, you could treat with an exonuclease that would degrade any cut plasmid but would leave supercoiled plasmid intact.