to point high-power radar-reflection surveillance satellites at certain empty reaches of space
That isn't going to work for stealth spacecraft which are a trivial engineering problem next to propulsion. Space is huge, you're going to need very very powerful sensors to find anything the size of a ship.
It's not that big, about 40,000 square degrees for a full spherical sweep, a wide angle lens is 100 square degrees, so call it 500 exposures. Assuming the crew have turned off everything except life support then it'll be radiating at some 280 kelvin against a background of nearly 0. Which is good and bright in the thermal band. But to be conservative we'll assume that it needs a full minute per exposure, that's
Of course the real situation is much simpler than this needle in a hay stack approach. Presumably you know who your enemies are. So you know where they are coming from. There a basically 2 ways of getting from A to B in space. Transfer orbits and continuous thrust maneuvers. Transfer orbits greatly limit the amount of sky to be searched. And something thrusting continuously is going to be a lot lot more visible.
Time is nature's way of making sure that everything doesn't happen at once. Space is nature's way of making sure that everything doesn't happen to you.