I have had a website and a LinkedIn profile for over a year that make this fairly clear
It doesn't work like that. You LinkedIn profile might easily land you any job in Software development, but not consulting.
In my opinion, if you want to do consulting for big corp. you should figure out what it takes to it. An attractive website and presentation, few buzzwords, client testimonials, business cards, and the other blablabla. Yes, it's irrelevant (and shitty) to what you are actually doing, but that's actually the world of consulting.
I think you can go further than that. To get people asking for your time as a consultant you have to demonstrate experience and get close to vendors who already support clients you are interested in. For example, targeting a niche "big data" problem with a particular tool, and then developing a relationship with the community supporting that tool. That gives you access to the people who are looking for consulting.
I hope you are right. If you are, you have identified a potentially very, very lucrative option for a start-up. Broken markets can provide you a lot of money when you fix them.
This market is already (at least partially) covered by small consulting shops which provide sales front for competent freelancers who don't feel like doing the whole corporate networking&sales ritual.
Well, the companies I know tend to do their recruiting based on word-of-mouth recomendations - so they have to know you from some previous job or you need to be recommended by someone etc. It's a tiny sample of a couple companies though, and that probably doesn't generalize to all "small consulting shops".
It doesn't work like that. You LinkedIn profile might easily land you any job in Software development, but not consulting.
In my opinion, if you want to do consulting for big corp. you should figure out what it takes to it. An attractive website and presentation, few buzzwords, client testimonials, business cards, and the other blablabla. Yes, it's irrelevant (and shitty) to what you are actually doing, but that's actually the world of consulting.