Slim HTPC PSU

Greetings Experts!

I'm building an HTPC in a slim case and looking for a +350w PSU to fit it. The case size is non-negotiable (has to fit in a tiny little shelf below my TV).

The case comes with a 270W PSU. I'd like to throw in a decent low-profile gfx card, but most of them need more oomph from the power supply, so I'm prolly gonna upgrade it.

The included PSU appears to be TFX form factor -- in fact I believe this is the exact one. Measurements are roughly: 6.7" long x 3.3" high x 2.5" wide. There's room in the case to get about an inch wider and several inches longer.

So I guess my question is... does a PSU exist that'll fit this space? I've found several 300w PSUs and will go with one of those if I can't find anything better.

Also, I'm willing to drill and cut to get a fit for something that isn't exactly the right size. However, I can't really compromise on height... this baby needs to fit on a tiny shelf in my entertainment center.

Finally, if I can't find a better PSU -- any recommendations on a gfx card that'll work well on 300w-ish?