I have a tv in my garage where I smoke with full cable. It's awesome! Don't know much about projectors, but they do make tv's specifically for outdoors.
Sell the z and buy the tv.
Amazon has some reasonably priced options.https://www.amazon.com/QKK-2400Lumens-Mini-Projector-Smartphones/dp/B07HT969MR/ref=sr_1_1_sspa?ie=UTF8&qid=1548789463&sr=8-1-spons&keywords=outdoor+tv+screen+and+projector&psc=1https://www.amazon.com/Projector-Screen-100inch-Projection-Activities/dp/B07L3LGSLN/ref=sr_1_2_sspa?ie=UTF8&qid=1548789463&sr=8-2-spons&keywords=outdoor+tv+screen+and+projector&psc=1Add a sound option and you are in the movie biz