Delete sitewide to recover from Penguin?

Hi all,

I am running a network of 15 niche sites, and haven't done anything edgy in terms of spam linking in comment fields etc. but the sites are linked together with sitewide links, all together this is several thousand links that uses the same anchor text.

My main focus regarding content have always been on quality and I believe that because of that, I have always seen a steady gain in visitors. Well, that was until May 22nd 2013 when the Penguin was realised, and I discovered a 20-30 % decrease in visitors. The same happened on Oct 4th 2013 when I saw a further drop in visitors and ranks.

I know that the drop probably happened because of several factors, but regarding the sitewide links, what do you suggest that I should change? I believe these links are good for the user functionality, so I don't want to remove them completely. I see several possible solutions:

- Make the links no-follow
- Send the user to a script which redirects the user to the right link
- Implement the links with JS/jQuery after page-load

Do you have any suggestions for what I should do?

Thank you all for reading and commenting!