I recommend to do two things. 1st follow your business objectives. If you really don't have any, then try writing it out. 2nd, and equally as important, optimize for your audience, not for Google. When I hear newbies talk about putting KWs in h1 tags and domains, they are thinking the wrong way. Don't be like me. I wasted time trying to optimize my website so much that it was over-optimized and unreadable.
I stand by my statement, KW in subdomains do not give a boost. If it did, all of us on MOZ would have done that years ago. It would have also created a lot of spam sites.
Do you have any comment on removing the keyword from the homepage content?
I don't know what your GA says. That's your call. If the keyword is not as relevant, then no. All the sites I have ever built had a home page that was about all the landing pages. Go to my site and study it (the shipping one).