Absolutely sign up for the Touring Plans Reservation finder. The service found me a 5:45 BOG dinner on the exact night I wanted it for later this month. Never thought it would happen.
Also, another idea, and not sure if you have young children or not, is to look at really late times. For instance, I couldn't find anything when I searched for dinner, but when I clicked into BOG and searched that restaurant specifically and entered 9:00 pm, a 9:45 popped up. I grabbed it as I have 2 teenagers and a pre-teen and it was an EMH night so we were going to be in the park late anyway. I figured we could make it work. I don't think this strategy would work with little ones, but if your kids are a bit older and can handle a late dinner, it just may work out.
Good luck and don't give up hope, you'll get it!