Any particular reason you picked the SLS? I'm betting price, but perhaps it was something else. Hope so.
Here's the deal. The SLS system, as good a deal as it may seem, is pretty much junk. Sorry, but anything these days that doesn't include HDMI is next to useless. Really. What did you expect from a 5.1 system with receiver and free shipping for just over 400 beans?
But there are some options: You can probably get pictures to the Epson by connecting component video cables between the source device (X-box, DVD, etc.) and the SLS using component video cables, then go out of the SLS component video outputs to the component video in on the Epson. It's actually going to take 3 individual cables for each connection, usually bundled together somehow so they end up exactly the same length. But here's the problem. If you plan to play Blu-ray discs, and with the 8350 and any screen of a size it would work with, that's what you should be doing, you're going to get shot down because BD needs HDMI for something called HDCP, which is a form of copy protection. What happens is the player says to whatever it's connected to, "Hey, I'm a BD player! What the heck are you?". The device needs to answer "Hi, I'm a display!" or "Hey, I'm just passing the signal to a display!" If the player gets that replay, everything works. If the player doesn't get that answer, it's not going to play a good number of discs. Not at all.
If your DVD player has component outputs, that will work with the SLS, but it's not typical anymore to have them. If a device you're using doesn't have component video outputs, you're kinda screwed. You'd get a basic picture using the composite video jack, but it's very low quality, and your 8350 deserves a whole lot more.
As a work-around, you could connect your HDMI sources to the Epson directly and then, if the source has an analog or optical audio output (that will work at the same time as HDMI), feed that to the SLS for sound. It's a kludge at best, though, and you'll pretty much hate it right off the bat. Add to that work-around an HDMI switcher from Monoprice.com (that's where you'll get the component video cables too), and it might be sort of workable.
But really, man, ditch the SLS, get an entry-level system with HDMI ins and outs. You'll be glad you did.