I would say go with a school-specific recommendation letter if you can get one - i.e., the professor is an alumni or a guest lecturer at your top choice law school, etc. This is your time to set yourself apart from other non-autoadmits. While a general letter may be more convenient, if this is trully your top choice you should make some effort to seek out someone with a connection to the school who will say you are a good fit.
Is there an option to have an interview with the admission advisors? That might be a good way to show your interest and dedication (provided it's not a cross-country trip for you).
As far as 2nd letter of continued interest - if you don't have anything new to say, I wouldn't do it. How about writing an application update letter - this is what I've been doing since I've applied - new volunteering projects, publications, school grades, etc., etc. This gives them additional reasons to change their mind and accept you
Hope this helps somewhat - I'm in the same situation, waiting and praying for acceptance after deferral. Good luck!