Do you really think a "net" would serve the purpose? You ARE right that the upper and lower bounds of a "net" would HAVE to travel at differential velocities to remain in orbit (invalidating the concept at one go), but you are SO dead wrong about "space" stretching "between 62 and 220 miles."

FYI, if you DID put up a net that stretched from a high to a low orbit, it would soon also "autorotate" due to the differential orbital velocities, and unless it were magnetic or some such, it would spill its cargo with every spin.

FYI2, This has been a concern for NASA for quite a while, and a "net" was one of the first concepts they realized would not work.