I have read several articles lately that discuss returning to the blue book as a means of keeping students from cheating on tests.  That is one option, and it may not be a bad one under certain circumstances.

If work is done in the classroom with no devices the students have to demonstrate their knowledge. Of course, that would mean you can’t use class time for teaching, so there is definitely a sacrifice if that is the route you choose to go. 

Why not turn it around? Instead of homework, their hours outside the classroom are spent preparing for the upcoming class.  We know they are not doing this now, but once in-class performance and grades are tied to it in a very tangible way, it may improve.

Another option is to provide specific guidance in the use of AI, even requiring a specific AI program and identifying which things they are allowed to ask for from it.  Require them to include their prompts as part of the assignment.  You will have to test the assignments yourself to know what responses they are likely to get from the different AIs so you can pick the right option.

Neither of these options reduce your workload, but they both increase student knowledge.  The second prepares them for the future where AI is a routine thing.