Does it take a while for new spark plugs to kick in?

No, unfortunately if “bad spark plugs” had been the problem - the new spark plugs would have repaired that upon installation and it would not tak a while to do so. There is another failure here - the only way to find this failure is by *hands-on* testing.. However I think you're on the right page - I too suspect an ignition misfire is the issue.. Likely one of the coils that sits on top of each spark plug - must be tested to confirm.