Architecture advice for converting biz app from old school to new school?

Question

I've got a WinForms business application that evolved over the past few years. It's forms over data with a number custom UI experiences taylored to the business, so I don't think it's a candidate to port to something like SharePoint or re-write in LightSwitch (at least not without significant investment).

When I started it in 2009 I was new to this type of development (coming from more low level programming and my RDBMS knowledge was just slightly greater than what I got from school).

Thus, when I was confronted with a business model that operates on a strict monthly accounting cycle, I made the unfortunate decision to create a separate database for each accounting period.

Also, when I started I knew DataSets, then I learned Linq2Sql, then I learned EntityFramework. The screens are a mix and match of those.

Now, after a few years developing this thing by myself I've finally got a small team.

Ultimately, I want a web front end (for remote access to more straight up screens with grids of data) and a thick client (for the highly customized interfaces).

My question is: can you offer me some broad strokes architecture advice that will help me formulate a battle plan to convert over to a single database and lay the foundations for my future goals at the same time?

Here's a screen shot showing how an older screen uses DataSets and a newer screen uses EF (I'm thinking this might make it more real for someone reading the question - I'm willing to add any amount of detail if someone is willing to help).