When you say cheap, the atom machines come to mind, but you said you're a power user, and that, along with my doubt that there are any with HDMI out, I'm thinking the really cheap ones are going to be a no-go for you. That said, there are devices cheaper than the Surface Pro line. My wife is using the Lenovo Yoga 11S that I bought last fall. It has the i5 Haswell, 4GB RAM, 128GB SSD, HDMI and the screen flips around to use it like a tablet. I gave it to her when I got my SP2, because I decided it was heavier/larger than I wanted. Now I'm on an SP3 and LOVE it.
I'm sure there are others, but I'm thinking that any of the convertibles or anything lighter than the 11S are going to be more expensive. I think I paid $750 when I bought it. When you shop, if that's the model you decide to go with (and I won't be in any way offended if you don't like it), make sure you get the one with the Haswell, as they did make this model in the third generation as well. I haven't looked lately, but when I bought this one, the only place I could get it was at Worst Buy. Lenovo.com was still selling the third gen but not the fourth.