Have you tried/considered the screen extension feature in the Windows 10 Anniversary Update?

Huh, I never even knew about this. I guess you mean this under the title "How to Mirror Your Windows 10 Screen to Another Windows 10 Device": http://www.laptopmag.com/articles/turn-windows-10-pc-into-wi... I wasn't able to get it working yet, though.

I haven't used it myself (no second Windows 10 PC), but that sounds correct.

I believe it's designed to let you use your Surface as an external monitor with pen/touch support for another Windows 10 PC.