What happened to VIA and their x86 CPUs and mini-itx platform people used to build media PCs on? Wouldn't that be a viable option if you really want to avoid ME?
VIA is 100% a viable option—they support SSE 4.1, run Windows 10, and their integrated GPUs even run DirectX11 natively¹—except that they compete with Atom, not desktop or even regular laptop CPUs. However, the current (40nm Isaiah) “high-end” VIA microarchitecture is a out-of-order, 3-fetch 7-dispatch wide² superscalar, fully pipelined core. So it should outperform a modern Atom by a decent margin, with only slightly higher power consumption.
Apparently VIA is still fairly popular in China (and by virtue of being a Taiwanese company, possibly Japan as well).
1. See e.g. http://www.viatech.com/en/boards/mini-itx/epia-m920/