I am using SSI and (temporarily) I am including the header, meta, and some formatting tags in a global ssi file for use on the entire site. Would that lead to robots deeming it all duplicate or punishably similar content?
No. Why would it? You are only duplicaing the the <head>. I take it that the content is different on each page.
Any SSI files included in a page are rendered as a complete page, to both visitors and bots... no need to worry about duplicate content