I am an honors graduate (top 20% or so) of a top 50 U.S. law school and published editor of the school's law review. My job prospects are not where I want them to be -- bottom level Vault firms at best. Would applying to an LLM program improve these prospects? If so, which one? Please help!! I'm at the end of my rope.

I'm not sure if applying to an LLM program would improve your prospects, but there are a few JDs (less than 5 though - im not exactly sure as to the number) in the current HLS LLM program. From my interactions with them, the main reason is they want to do a career shift. Are you shifting tracks, or do you just want to get to a top tier firm?

I'm only a year out, and I've spent most of that time clerking for a judge. So, a career shift is not really what I'm after. Really, I'm just frustrated with my prospects. Does the "Harvard" label seem to help them? What about access to career services?

A top 20% editor of law review at a top 50 school clerking for a judge; good job. I don't think an LLM is going to help you. I think if you get a good head-hunter and keep at it, you'll find something better. Depends on what you consider "good" as a prospect. Most LLMs are fulltime, and I strongly believe that another year of big firm (even if not "top" vault ranking) experience is just as marketable if not more so than a domestic LLM. Of course that's not true for academics, career shifts, clerkships, etc, but from the big firm's perspective it is true. So you'd do better making money working for a year and trying to lateral than spending money on an LLM. (If you want to do one part-time (i.e. NYU) in your spare time, then maybe that's something to consider).
You need real advice. Email a couple hiring partners at the firms you think are "good" prospects and ask for a quick opinion on the subject.

Thanks for the advice on contacting a hiring partner. I'm really just after a top 50 Vault firm, although top 25 would be even better. Can I secure access with an LLM? Anyone else have any thoughts?

Unless you want to do tax, an llm is far from a path to a prestigious job, especially for someone with credentials such as yours. If you look at the career services site of most law schools you will notice that non-tax llms do not receive a lot of assistance in the form of on campus interviewing opportunities and have to do the majority of job searching themselves. To me this says that employers are not very interested in the llm degree. Even for tax llms, the degree is important but a candidate's JD institution and grades still weigh as heavily if not more in decisions to grant offers.

Instead I would look into why you have not been able to secure the type of position you want? I know of many people who have credentials similar to yours that have not been shut out from the type of firms you are looking to. Try to figure out what possibly could be holding you out then improve that quality in yourself. At the same time excel at the so called lesser firms that are willing to hire you, and you will have no problem lateraling to a more prestigious firm.