My strategy was to tell them something like "First I'm going to interview at all the companies that don't require take home assignments, and then I'll get back to you if I don't have a job by then".
This. Happened with my most recent round of interviews. I took an initial stab at one assignment, moved onto other opportunities, and landed an offer before getting back to the project work.
At least the take-home work I did perform in my second-to-last job search provided good, compact example code for my last search.
