I spent an enormous amount of my childhood & early teens looking out the window of my father's Cessna 337. I found that to look as close to vertically down as possible is actually quite unnatural, the eye will unconsciously keep fixating on details & then whip-panning to the next random detail. The fovea (the surprisingly small area of decent vision our eye has) is designed to continuously move around building up an image & correcting what the brain thought it saw.
Our image of the world is not actually what the eye is looking at, it's what our brain puts together in the visual cortex (optically, it should be upside down for example, but the brain corrects this). Try moving the focus of your gaze, at an even speed, over a patterned carpet from different angles & you'll see what I mean. If your brain doesn't think it's important, it won't bother resolving it properly. Finding your girlfriend's earring in a place you've already looked at eight times is down to how we perceive.
I found it a constant battle to look at areas totally objectively when looking for particular things, and not allowing myself to see just what a part of my brain expects to see. Having a fixed image in your mind of what you're looking for can impede your ability to see a variation of it. I found that it was more tiring the more you limited your scan to straight down, even though it's theoretically closer.
I reckon somewhere between 30-40 degrees from vertical, with constant "situational" general scans. But it needs to be a methodical, yet natural, scan pattern.
As you say, professional military or civil ASR personnel will be the only ones able to answer this properly. They should be able to advise the best relationship between altitude & airspeed for example.