IMHO Static home pages are pretty much a waste of time for both google and the user. There was a trend many years ago to have a welcome page as the home page, most people are too busy and want to get to the meat of the site without having to reading welcome to my site blah blah blah. If that is your home page then my advise would be to seriously think about updating it to something more dynamic which would give google a reason to index it more regularly. If it never changes as you suggest then Google will learn it does not need to be checked as often.
As for including a snippet of the main blog post, This is something blogs do all the time, I stand to be corrected but I doubt that would have a negative effect but supplying your home page with fresh regular text would be of greater benefit.
Good SERPS is great, Traffic however is even better