Your EPIA is most likely CPU-bound when playing back video. 1080p playback is very demanding and needs a fast CPU.
Your best bet might be to get a low-end discrete graphics card that can do hardware decoding. The nVidia GeForce GT610 is available in a PCI version (assuming the EPIA doesn't have a PCIe slot) and is well-supported on Linux, including hardware video playback via VDPAU. They are almost always passively-cooled and usually come with low-profile I/O brackets (although you should double-check this before buying).
Hope this helps,
Stephen