It's 1000 knots and 60,000 ft, and this is only to meet U.S. ITAR export requirements. There's nothing inherent about the civilian GPS signal itself that prevents you from computing a fix beyond those limits.
and then design a baseband yourself. I'm currently aware of at least three people that are working on this or have already done it. You'll need to actually take the time to learn how GPS works, and it'll probably take you about a year, but it's definitely possible.
It's called COCOM limit (historical reasons), and you can have it turned off at the factory if you can talk them into it / have a valid reason to. Oddly enough "we want to send up a small satellite, and we are calling from a NASA facility" was not a good enough reason. Surprisingly GPS will work decentish in LEO, if you can get past that. The GPS satellites are in semisynchronous orbit.
For example, you could buy one of these: https://www.sparkfun.com/products/10981
and then design a baseband yourself. I'm currently aware of at least three people that are working on this or have already done it. You'll need to actually take the time to learn how GPS works, and it'll probably take you about a year, but it's definitely possible.