Three things- 1- You do have to call them directly, but it may be that they don't take reservations for dinner possibly? I haven't called to make my reservations yet, but hopefully they will allow you to make them! When you find out will you update us so we know for future as well?
2- Add yourself to their email list and use a family member to put it under that has a birthday before you go. I signed up because we are eating there in December and my birthday is in July and they sent me a coupon for a free kids meal (SCORE since we are eating with a kiddo) or a chef's choice appetizer as long as you buy an adult entree (we are traveling with 3 adults so that isn't a problem). I looked at the email and there is NO expiration so I am printing it out and saving it for December hopefully you can do the same!
3- Its worth looking at the Landry's club to join as well- it costs you $25 (not a year, just one time) and you immediately get $25 to use within a year of getting your card. You accumulate points at RFC as well as other places, can get a discount at the retail parts as well. Plus the month of your birthday (my mom is in December so the card is going in her name) you get $25 to spend every year- so for $25 we are getting $50 to spend on RFC- total SCORE!! If you can work it out so you go within the timeframe of one of your members birthday month (or I believe two weeks after the month) you can get a killer deal on your dinner there which if you have 3-4 people or get a dessert will easily hit $50 or more. GL and let us know how the ressie worked for you!