Finally made the four strains MIV-competent today.
I still think the overnight method is faster, though, because you don't have the additional step of growing cells to OD600=0.1, which takes an additional day.
I also ran another PCR today, and not even the Good Luck Crystal could help. What is the problem? I added all the ingredients (I even checked them off as I went) in the correct amounts, and the cycler was set properly...
I found an online PCR troubleshooting guide. Hypothesis A ("Pilot Error") and I ("Bad Karma") look especially promising. Will read the page and try again later.