In an ideal world my opinion would be to have it all on the one domain however given the problems with this you've stated it seems the best low cost alternative.
It wont harm SEO efforts by having the blog on a subdomain , however I don't believe Google will attribute the full value of links to the parent domain as it would if it were all on the same URL.
I don't really understand the point about the wordpress.org hosted blog however as long as the URL's resolves as the sites URL then it shouldn't be a problem either.
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