Before I moved from Texas... UFC and Boxing PPV and the occational big sports event were always outside... Ice chests full of ice cold beer and running grill hot, with pounds of meat... friends and family... the good ol days...
I never had a problem with bugs, with the projector... they loved the screen though... I considered making a little box too, I never did... but I was more concered with possible rain...
As for your idea of shooting it through the window... I'd go with that! I didnt have that option... I had street lamps too... and the lights mysteriously getting damaged around fight night got incresingly odd... anyhow what I was gonna do was go wireless...
I had a cheap old stereo for sound, that I could care less about... but wireless for the projector... was my real concern... you can even get wireless speakers too...
All the wires are like a magnet for drunks, kids, and stupid people... plus putting stuff away would be easier...
I'd go with the widow idea, even if you get the projector wireless... I know that you lose some of the clarity, but someone drop kicking the projector could get be even more ugly...
I even dug a pvc pipe with extention cord into the ground to minimize the cords too...