If a restaurant is small and has a rotating menu of sorts, will I piss them off if I call and ask when a specific item will be served before I make a reservation?

If you phoned the restaurant and explained to them your situation as nicely as you've done here, any place that would make you feel like an "unsophisticated idiot" doesn't deserve your money. The only issue I can foresee is, if the item you seek is indeed seasonal or by availability per their purveyor(s), it may simply be hard for them to gauge that far in advance. The only pragmatic suggestion I have is to go ahead and make your reservation early, but perhaps have a second option lined up as well. And then about a week before your reservation date, phone the preferred restaurant again and see if it's likely they will have the items you want on the evening you plan to dine. If not, canceling your reservation with a week's (or even just several days') notice will likely not affect them detrimentally. If the person who answers the phone seems dismissive, ask to speak to a manager. Explain your situation, and then give the manager time to consult with the chef. Leave your phone number so he/she can phone you back. But whatever you do, do not call during the "height" of service; try to schedule your call around 5:00PM. Of course, you could also try making a specific special request (tell them it's for a special occasion), but then there's the possibility you might incur an extra charge. Hope that helps.

Most restaurant owners would be tempted to perform a criminal act in order to get the sort of feedback that you are hoping to provide them with. Everyone else here has already given you the answers you need. Go ahead and ask, you have nothing to lose and everything to gain. If they accommodate your request without charging a premium, please make sure to tip generously and send your compliments to the chef. If anything, sending a bottle of wine into the kitchen is a gesture that's always appreciated.

I have a restaurant, and quite frankly, if you ordered well enough in advance (to allow us to buy raw materials), and you accept it might cost a little more (as we may not be buying that item in bulk), then we will pretty much make you any food you like. We can certain revive a dish from a previous menu. Restaurants are about giving great service. Any chance we get to do something difficult is an opportunity to show that. In short (as all marketing theory says) if we exceed your expectations, you will become a proactive ambassador for us, the most valuable thing that any consumer service business can have.

On the contrary, it will display to the staff that you are familiar with their restaurant and how it works.  That you enjoyed a menu item so much you want to ensure you are timing your visit correctly is actually very courteous to the restaurant, rather than what most people would do- not bother to learn that the menu rotates, showing up whenever, then complaining when the item in question was not on that day's offering.As long as you're polite on the phone, the staff should have no problem letting you know.

If you make a call like that it's basically telling them "I will show up and spend money when you do [thing]. Can you tell me when that will happen again so I can give you more money?"As a rule, businesses are big fans of people who give them money. I imagine they will be happy to tell you when you can show up to give them money.