^^^THIS^^^ is where I was going to go with my response.Where are you measuring to on the seat post/saddle? The accepted reference point is the seat rails, so is that 5.5" (140mm) from the top edge of the seat clamp to the saddle rail?
You also don't mention if the frame has cable routing for an internal dropper or not? If you need an externally routed dropper this will eat into what you have to play with.
Based on your post and some quick searches, it appears you need a 30.9mm internally routed post that will allow for 140mm from the bottom of the collar/top of seatpost clamp to the seat rails in the extended position while requiring less than 135mm of insertion to do so. For the most part, what you are looking for is a unicorn and you'll have to go to really short travel.
From what I can tell, the following brands have nothing that will meet your needs...
PNW, OneUp, TranzX, KS, BrandX, Bike Yoke, Crank Brothers, Fox, Race Face, Rockshox, SDG, e*thirteen, DT Swiss, Thomson, Ultimate USE, Manitou, Ritchey, FSA, Easton, X-Fusion, Pro Bike Gear... I think you get the idea.
The 9point8 Fall Line R 275x75 comes really close, but still appears to exceed your maximum dimensions slightly.