An LLC might not be able to hold an ownership interest in an S Corps and, although an S Corps could potentially own an LLC, there are tax issues to consider.
Whether or not an LLC can own an interest in an S-corp is irrelevant here since he owns his S-corp shares as an individual. There is nothing prohibiting an individual from owning shares in an S-corp and owning a separate LLC, even if that LLC has a licensing agreement with the S-corp.
What you might want to do instead of starting your own LLC is to address with the S Corps board of directors what you see as the potential for the product. The company already may have plans in mind for the product.
It sounds like they are already past that. The OP is the second largest shareholder in the company. Do you actually think that he is out of the loop?
I recommend you seek a personal review by a business law professional in your area to discuss what you can and can't do as shareholder in the S Corps.
Good luck.
Just as an FYI, owning shares in an S-corp does not restrict an individual as far as their other investments are concerned. Yes, S-corps are restricted as to who can own shares, but that has nothing to do with what other investments an individual might have. Those restrictions (as applies to individuals) are related to citizenship.