I don’t recall changing my forms for a larger number of props, its more about the procedures. If anything it is even more crucial that everything is documented and a system of double-checking is in place, because you can’t rely on memory for 200 items. My best advice is to rely on systems that have been successful for you in the past, adapting them as the specific situation demands. For me, that means all the props that need checking are on someone’s pre-show list, and they are on the run sheet in instances where a crew member is involved in doing something with them during the course of the show (handoffs, resets, whatever). I start making these lists as blocking begins. I only use a Prop List in early rehearsals to track whether we have the actual prop from the designers or not.
I do often use a scene-by-scene in rehearsal, as well, the way Megf describes. I'd build on her idea by figuring out what props are set-dressing type props that won’t need to be set on a daily basis (lamps, rugs, books on shelves, etc). It's worth talking with the designers about how they can be creative in securing props to the set, or to each other, if that’s helpful for running the show.
Another idea to think about is taking photos for reference on complicated pre-sets. This worked well for a show with an intricately stacked pile of chairs, and we had three assistants each responsible for a certain section of the “formation”. Photos can be too much trouble to take, update, and flip through with props that are easy to identify and set properly, so just don't make your life harder doing this.
Loebtmc’s suggestion of using your crew creatively, drafting in everyone from board ops to dressers, is crucial if staffing is a concern. I’ve worked on some pretty intense intermission shifts that seemed impossible at first but became manageable with practice and extra hands from the booth. Costume crew can become responsible for personal props or costume-props that come out of pockets or are naturally acquired in the dressing room (umbrellas, money). I’d also look out for items that are a lower priority, and can be checked (and efficiently corrected if needed) after the show has started, or as an actor comes to standby at the stage for the show. I’ve had shows where I ask the ASM over headset “does Actor X have Prop Y in left hand?” for an especially elusive element. Another idea that's worked for me is to check that a number of props for post-intermission are just all in one spot, then have an intermission check-list for moving them onto a prop table or other convenient position.