My suggestion is to try AJAXing the tabs. If the outbound links are more of a concern then the keywords of the link, AJAX loading of the tab content would remove them from consideration. Google won't index content pulled in from an external source.
However, be careful to put a rel="nofollow" on the link that loads the content as you don't want SEs indexing the source.
Do not put a meta nofollow in the head, it will kill all links on the page and seriously mess up your link flow. Your use of rel="nofollow" is correct in the context of the specific link tags.
I wouldn't sweat the shear number of links - the 100 count is a left over from the days when spiders only downloaded 100k from the page. It has since risen to the point that the practical limitations of over 100 links is more pressing (IE, do you visitors actually value and use that many links?)
If each link is valuable and usable, no need to worry. If not, perhaps there is a structural way to reduce the count.
Also, load the footer by AJAX onscroll or on demand. Assuming all of the pages can be found in the top navigation, the bottom links are just exacerbating your issues. Primarily, this section is giving far too much weight to secondary or auxiliary pages.
For instance, your Privacy Policy only needs to be linked to where privacy is a concern (ie the contact form). Good to put it on the home or about pages too if you have a cookie policy.