First off, stop calling it an idea. (might be just that, but in licencing efforts you don't want to call it that).

Second, what do you mean time is of the essence? This already started sounding risky.

With that said, I believe you have two options, assuming that you can spend the next quarter reaching out and performing poorly in presentations and pitches to executives for licencing deals.

1. Learn the art of pitching and presenting, in my blog I have listed some books, one of them is presentations like Steve Jobs. Check it out here: unthinkeverything.blogspot.com (books are listed on the right) and hopefully secure a deal. The risk with this is that if you don't is time wasted.
2. Figure out a creative way to launch your innovation yourself, even if is simply to test for validation. It can be relatively inexpensive to do this (you didn't provide information on your patented idea so I can't help you on that yet). The upside of you launching your product or validation effort yourself is that it gives you exposure, it gives you business experience and most importantly it adds tangible value to your idea no longer putting you on the spot putting a random price point for it. This also makes it easier for you to approach companies and executives and if the licensing deal doesn't go through you have a business out of it. The reality is that if another business can make profit off a license, so can the owner of the product itself. Just have to figure out how.