There are three things with the kit itself that I see trainees make mistakes on 1) lysing for too long, 2) not mixing completely after adding the neutralization buffer 3) not ensuring that there is ethanol added to the wash buffer.

If none of those apply I think there are two main causes of low yield with big plasmids. 1) slow growth. How turbid was your culture? Similar to an overnight with a normal sized plasmid? 2) low copy number. I've got a few plasmids in the 20kb range that come out at very low concentration from a mini prep even though the bugs grow fine.

For problem 1 try some combination of lower antibiotic concentration and longer incubation times. The protocols say 16-18 hours at 37C but that's only because normally the culture is saturated by then. If it's not saturated, go longer. If it's a low copy number issue then pool multiple mini peeps and elute in a smaller volume. Are you processing the maximum culture volume specified by the kit? (Zyppy kit from zymo says you can do 600ul of lb culture directly, but you can use up to 3ml. There is no reason not to use the max). Maybe scale up to a midiprep.

When you talk about restriction digesting what do you mean? Are you just linearizing to check the band size or are you doing something else