IIRC, the Kuiper belt is roughly aligned with the ecliptic, although I'm not 100% certain of that. The Oort cloud, however, isn't. As its name implies it's not confined to a narrow range of orbits like a "belt"; the cometary orbits have no relationship to the ecliptic. They effectively form a widely dispersed sphere which extends hundreds, maybe thousands of AU's from the system primary. This is truly a vast volume of space. Mr. Tyler's estimate of "thousands" of ships required to patrol the Oort cloud may be a few orders of magnitude short. Anybody got a few spare von Neumann machines?
Regarding jump flash; as I understand it, this signature is considerably larger than that of most starships cruising sublight, let alone running silently. In most cases, a ship jumping into the Oort cloud will arrive a long way (several AU's, barring plain bad luck) from any hostile sensors. While the jump flash is detectable over many AU's, actual ship detection requires shorter ranges. It will be many minutes, possibly a few hours, before the jump flash is detected, and there are several ways for the intruder vessel to take advantage of this.
1) Arrive with a high sub-light vector, and run silent.
2) Accelerate to a high vector before being detected, then run silent.
3) Arrive close to a fuel source, refuel and jump before local forces can respond.
Option 1 works well, unless the locals analyze the jump flash well enough to guess the intruder's vector. Is this even possible? (My PC's keep hitting DC50's!) Option 2 prevents that scenario, but if there's a local ship close enough to see the intruder maneuver, he's better off running silent. Option 3 is tricky--the intruder needs to refuel
fast, and the locals will see the jump flash when the intruder leaves, so repeated use of the same refueling source by the intruder means the locals will eventually find it.
Cat and mouse, ad infinitum....
XO