Not so sure engagement programs are the right way here. All depends on how you want to market to these leads, but if you decide to do one engagement program per category..i forsee some roadblocks.
Leads cannot be active in more then one engagement program to my knowledge, so this complicates things A LOT.
I'd suggest rethinking the nurture if this is true, or using the "older' nurture method with traffic cops to monitor leads in various programs.