First of all, congratulations on your anniversary!!!
Second, I'm sure somebody here will offer you an amazing suggestion. My suggestion is not based on any restaurant in Rome, but more on having been married a billion years.
IF something happens that day - a cab strike, a bus delay, etc. - and for some reason you can't make it to the restaurant of your choice on the exact day of your anniversary, treat yourselves to a dinner at a place that looks good to you. You and your loved one will be together IN ROME. Seriously. How cool is that? And if for some reason, your anniversary day plans are changed, you can always have the extended celebration tomorrow. The next day. The day after that.
We've leaned from years of experience, not to put too much stress on the actual day of any celebration. If something doesn't go to plan, you can always celebrate again...and what could be better than celebrating twice?
Have a great trip, and happy anniversary to you both!!