First of all, I like your new design, and typically, large sub-navs are excellent for usability and spidering. As Michael Martinez from seo-theory.com once eloquently put it: "[PageRank] was made to be wasted. Real SEOs understand that."
If you think of your homepage as a balloon and PageRank helium, then trying to capture as much PR as possible to increase rank seems logical. Unfortunately, that's not a correct analogy. If you've just re-designed your site, it's likely that there are new problems created you're unaware of. Or, also likely is that - depending on how new your site is - Google's system hasn't finished fully evaluating it. It's normal for a redesigned website to see some rank fluctuations over the course of several days (or even a week or two) while it is in various stages of being indexed in ranked.
Do not use ""style='display: none'" to hide links. This is cloaking in its most basic and easily detectable form, and whether you mean well or not, Google can't detect your intentions - so don't expect them to.
TL;DR I would recommend you re-evaluate the rest of your site first, your competitors, and link situation before worrying about too many links on your main nav bar as it's usually not the issue.