First off, the problem with NG certainly should not be you having too much work to do. Once the redesign comes out, what is there to do? The site, as said, is self sufficient. It runs itself! Your only job should be making in-house content and handig out monthly prizes. I can't actually understand what else there is in your work life.
So just leave NG on its own to rake in the cash, whilst you work on Behemoth games.
As for becoming dominant on the Internet, you've made mistakes in the past and I'm not sure what you can really do to make a "comeback" now. The biggest reasons why Newgrounds in its current state will not excel is the fact that you only host Flash, and a lot of the content is tailored towards the nerdy part of society - the gaming oriented crowd.
For example, you have a game on the home page that boasts some form of "physics". Even console release games don't talk about the game engine. People are simply going to see the word "physics" and make numerous assumptions about the site, and why it doesn't mean anything to them.
Also, YouTube and some of the other sites are owned by HUGE corporations - Google, News Corp - they can hire a million times the specialst staff that you can.
With that said, you're going to have to focus on strengths that cannot be copied or immitated on other sites. Right now, you can boast the fact that you have the most Flash content on the web. A site like YouTube SIMPLY CANNOT COPY ALL YOUR CONTENT, since they're a corporation. They have strict copyright restrictions. They're simply not going to be able to get copyright permission from the hundreds of successful Flash designers on this site.
And while you're at it, why not hop on the casual game bandwagon. Have daily sudoku, brain training, simple games. Not many people want to play a full length adventure game on the net. They want quick simply stuff to pass time. That content should be pushed to the forefront of the home page. and for God's sake, advertise it in an appealing manner.
And from a technical standpoint, make the icons on the home page bigger, have more big pictures and less words, use a white background.