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I don't really have an answer but just wanted to give you a thumbs up for the Ron Burgundy reference

Just a quick tip.

I wouldn't blindly post product links all over your social media platforms just for the sake of 'trying to affect your ranking' as more than likely it will come off quite spammy.

I would probably focus on more creative strategies of getting people to either share or +1 your posts and pages through unique content, competitions etc.

I imagine in the long run it would have much more positive implications for your main page's ranking.

From reading around the impression I get is that the update is removing some link weight from higher PR sites in order to reward sites with a diverse range of backlinks (to try and catch out those with tools getting links from a concentrated source or paying higher PR sites for links).

I think as long as you have regular, quality content and concentrate on getting links from a wide range of website types (that are relevant) then you should be fine.

I think this year it's v.v.v.v important to be active in G+ too once you have the icons set up as Robert suggested.

On G+ there's data that shows how the amount of circles you are in has much more of an effect on G's algo than the engagement from people with you in their circles (+1s on posts) etc (Sort of the opposite to FB/TW)

Do you get followers that are worth engaging with from this?

I just signed my personal account up and straight away got 10 spam like accounts following me

You say you have a feeling eMail with links to this homepage could be contributing.

If you have a recent campaign the emails themselves could have been misleading and lead to a decent CTR but then once people hit the page they weren't impressed.

Also have you noticed a high increase in referral traffic from any sources recently? Same principle could apply there.

What keywords are the homepage ranking for? Again people could be entering through certain phrases and then not seeing the results they were expecting