1. Should the whole site be optimized for local - appropriate schema markup, G+ business local set up, contact page with correct address formatting, building citations/local links etc.? To accompany our targeted page?
If you are going to target that area specifically, then yes. If you still want to maintain a focus on national or boader match keywords, then no I would not modify the whole site.
2. Will taking a local first initiative hurt reaching our non-local target market? If so will a very targeted landing page for local customers do the trick minus rest of local optimizations?
You have to remember what the landing page's purpose is. You are trying to rank for one or a few things in a very specific area. One challenge I forsee in just having the landing page is that you are going to be up against companies that focus their whole effort to that one given area.
Depending upon what your long term goals are would determine how you move forward. To answer your question, yes it could hurt you on your national focus if you change your entire site to focus on that one given area.
Another aspect to look at is PPC and AdRank. Since you will have a local page that is highly targeted, your ad score will most likely go up for that ad if you choose to go the paid route. More on that here: https://www.youtube.com/watch?v=MBmPtduElkM. If you are going to run some ads, the landing page could work well for you, and not be that expensive.
So what are your options? Well, IMO the landing page may accomplish what you are trying to do if there isnt a lot of competition for the phrase and target area. If you have competition whose main goal in life is to rank for that one area and phrase then I do not see the landing page carrying enough weight to make a difference.
If there is strong competition for that area, you may want to investigate a exact match domain, and place your content on that site. Many people discount the value of EMDs simply because they do not understand the value and their purpose. True, an EMD will not be easy to get to rank for a lot of keywords, but that is not their purpose. An EMD is to target one specific area and keyword. Will one page be enough? Probably not, but by setting up 5-10 pages on an EMD could get you ranking very high if the content and site are put together well. You could also link to your local site from your main national focus domain, and help them both out since they are relevant to one another.
By having the other domain, you dont risk sabotaging your main sites traffic by changing to a local focus. This will also allow you the freedom to create local profiles (citation sites, Google+ personal and business, etc) for your new domain. I know it sounds like a lot of extra work, but I dont think that having the subpage on your main site will be enough unless the competition is weak, or you have a lot of ways to promote the new page through marketing.