So the pitot tube is used to measure airspeed not altitude. there must be a seperate (reference) pressure sensor that you use for altitude. The relationship between pressure and altitude is well defined and if you have a good sensor you will get good readings (temperature compensated of course) What are you hoping to achieve with the RTK that you were not getting from the existing system? This sound like a research data collection project? What is the purpose, then we can work backwards to a solution.
Anything is possible. Putting an arduino in line between the Reach and your existing system can convert the nmea output (at 5 hz) to whatever format you wish or your existing system can ingest.