Yes, 301 redirect is the best option but remember 301 is PERMANENT! For temporary changes use 302.
I am a little confused why management wants to replace the home-page with the store page? I would have to know more about the company and the logic behind the decision (proof of why it would improve conversions). If that has not been explored through behavioral tracking I would be hesitant on doing the redirect.
Besides that you are correct with the complications. Remember is takes some time for Google to crawl the site index the redirect and give the trust and ranking to the new page. If you have a lot of traffic this will happen quicker. Also, keywords from the home-page will take a hit and change after sometime as well.
MOZ article about redirects, the best practices and installation.
Good Luck!