It depends on the LA. Many make their living on project management. Your project is not well suited for a higher profit margin, so is unlikely to get much interest from those who fit that description as it would displace a higher margin job. You can't blame them for that.

However there are many that do this sort of thing (I am one, but not in your area). You just have to pick up the phone and see who is interested. I think that it might take several calls before you find one who is willing to meet with you and write up a proposal.

Don't overlook good designers who are not LAs. It is a long, expensive, and difficult process to become licensed as an LA, so not so many people put themselves through that as they do not do major site planning and have little need for that broader skill set that is required to be an LA.

I'm in "upstate" NY and am a Landscape Designer. I have a AAS in Ornimental Hort from Finger Lakes Community College and an MA in LD from Cornell. Wish I was closer, because I'd help you. You might want to see if you can get an LD instead of an LA. You can be an LD with just an associate degree in Ornimental Horticulture where as LA's have masters degree AND has a state license. I never went for the State License. Don't know if Nassau Community College,any of the CUNY Colleges or Stony Brook have landscape programs, but you may want to check that out. Syracuse University and Cornell both have NY State accredited programs. You might be able to find a local college kid who needs the experience that can help you.
Also...you could also do is call your local Cooperative Extenstion office and talk to the director of the local Master Gardener Progeam. He/She may know of any Landscape Designers. If you don't know where your local CCE ofice is the main link is attached !
OR ...If you have a local garden center, see if they have some one there who does "side work". We have a samll family owned garden center chain here that has an LD and they are GREAT! No idea of the "big box " stores have people like that in their garden centers.

Here is a link that might be useful: Cornell Coperative Extension

"You can be an LD with just an associate degree in Ornamental Horticulture"

JJM: I am in NC. I have access to NC State University. I am 45 and considering my return-to-school options. It sounds like you are finding work with your degree and are satisfied? I don't particularly relish going into business for myself, but is that the only way to make a living?

Oops - I ran across something from the NC State website that should answer a lot of my questions.

http://www.ncsu.edu/majors-careers/do_with_major_in/showmajor.php?id=89

Here is a link that might be useful: NCSU website - choosing a major.

Not to be a PITA, but I would definately not hire a kid in college to draw up a 5 year landscape master plan. You'll get someone trained to draw plans and trained to gain from experience. Two great things to have moving into a career in landscape design, but not a great benefit to Melbo5.

Experience is going to get you a good plan. It is foolish to have an inexperienced designer do a master plan.