There is no problem daisy chaining GFCIs, I do it all the time with the cord mounted GFCI I use when I am working outside. The circuit has or is supposed to have a GFCI but I still like having one I monitor and test regularly. There is also a GFCI on my boat lift in addition to the GFCI feeding the circuit.
This is a very mature technology and I am skeptical of any claims of false trips unless the GFCI itself is bad. That is usually a hard failure. (won't reset, even with the downstream circuit disconnected).
You are right, it is beyond the code requirement but it should work fine.


Greg Fretwell