I wrote to the manufacturers of the EM-406 and they said that the limitation is built into the SiRF chipset, so wasn’t something that they could change (their hardware and firmware are at a higher level).
I am going to fly an experiment on the next Cambridge University Spaceflight balloon to test five different GPS modules at more than 30km and see which, if any, work. If you email me at hallam at mit dot edu I will send you the results (expect it to take a couple of weeks)
I also have about 20 units of the GPS-MS1E module, which is older technology. I’ve successfully tested it to 32km. It does draw a little more current than the EM406, it takes about 150mA at 3.3V and you need an external active antenna. Excluding the antenna it is a little bigger than the EM406 but not enormous. I can sell you an unused one for $40 if you like (I paid about twice that much a year ago…)
Henry