When I hold the guitar up standing...the most comfortable position I've found is to hold the neck angled up and the body down..so far anyway....and strumming straight seems impossible like that...
I'm wondering something, but, let me tell you my experience, then you can decide for yourself whether or not I'm on the right track.
When I first started playing I played sitting down almost exclusively. When I finally got a strap and started to stand while playing I discovered that I had been sitting wrong (too low to the ground which made the guitar sit up higher on my body which caused the neck to angle up). I figured this out after I realized that when I switched from sitting to standing there was a period of adjustment (just a minute or so) where I would try to hold the neck up at the same angle it had been when I was sitting (it also caused pain in my neck and shoulder from trying to hold the neck up). If I just let the guitar hang naturally, it threw my fretting off because I had my hand/wrist at a different angle than it was when I was sitting. (Am I making sense?) Anyway, I bought myself a barstool (and a footstool, but I'm only 5 feet tall, so I needed one!) and I began to use my strap (letting the guitar hang naturally) whether I was sitting or standing because it kept the guitar at exactly the same height and angle either way. Being up on the barstool, and using the strap, (or standing) I forced myself to "relearn" my chords at the corrected angle. I no longer have any periods of adjustment, my neck and shoulder pain has gone away and I have better left hand control because I'm not exerting any effort with it in an attempt to hold the neck up.
The main reason I'm even bringing this up is because of the quote above. You're right, it would be impossible to strum straight if you're holding the guitar at an angle. It's just a thought. Take from it what you will!