Unfortunately, Google views redirects to the home page as "soft 404" errors. It treats home page redirects the same way it treats a page that isn't found. You are likely not getting any SEO benefit from those redirects.
I would recommend setting up a separate landing page for these links. Setting up a separate landing page allows you experiment with the content without effecting the content of your home page. I usually find there are things that the home page needs that add clutter to a landing page and reduce sales. It is easier to experiment with removing things like prominent login and navigation. On your landing page your call to action can be front and center for your visitors.
I would also recommend using URL parameters for tracking inbound marketing links. That way it is easy to tell Google that they don't effect the content of the page. There are settings in Google Webmaster Tools for doing so. There are also parameters that are compatible with Google Analytics that Googlebot ignores by default. The "UTM" parameters start sessions in Google Analytics similarly what you describe you are already doing. Here is the Google Analytics URL builder that can help you create URLs with the proper parameters. Your new landing URL might be something like:
You could also use meta rel canonical link tags instead of using redirects. That allows you to have many pages, change the content somewhat, but tell Googlebot that the pages are all duplicate and that there is one URL that it should index in the search engine.