Seems to me that versatility is actually your greater selling point.

Yes, you could concentrate on 1 niche problem that you solve over and over again for various clients.

Advantage: That streamlined approach would be efficient in terms of presentation and actual work load.

Disadvantage: By promoting a very specific offering, you may be introducing yourself as the wrong tool for the job ... for most potential clients. If I stumble across you and find a landing page that stresses your ability to solve Problem X while I am dealing with Problem Y, then I assume you're less relevant than you might be. That does a disservice to your diverse skill set.

You can marry the best of both worlds. Here's what I'd suggest. Clients will discover you both passively and as a result of active outreach. So

1. For your active marketing efforts, identify prospects where the client really needs you for Problem X, in which you're specializing. Introduce yourself as a specialist in Problem X (which is true).

2. For your more passive, less keyword-targeted online footprint, showcase your versatility rather than your specialization. That's also true. This way, you'll seem like a better fit for a wider group of potential clients. Instead of writing you off as a specialist, they'll consider engaging you as an IT "renaissance man".

Narrow the focus of your presentation when you have narrowed your demographic. Widen that focus when the demographic is wider.