How to install a portable AC exhaust in a vertical window with horizontal blinds?
With a long enough vertical window adapter kit, you could likely get the exhaust hose port to be at the very bottom of your window. That would let you get your blinds almost all the way down, which might be good enough. There's really not much more you can do -- portable A/C units work best with a direct exhaust route to the outside, so any shenanigans to try and squeeze that exhaust hose between your blinds will reduce its efficiency and lead to sub-par cooling.

You could also use a special, sliding-window A/C unit (e.g. http://www.amazon.com/Frigidaire-FFRS1022R1-115-volt-Conditioner-Full-Function/dp/B00VV2JV3I), which might be able to fit behind your blinds.