If you look in the Atari documentation, the FPU cookie can return different values, a 68881 or 68882 etc could cause issues depending on what HB expects to find. Not to mention how well the author of HB interpreted the FPU cookie docs. If you have a CTxx then the FPU there takes precedence, the FPU on the falcon mother board is effectively not seen. FPU's built into 060s are a whole other matter, TOS does not support this. It requires patches to the cookie jar, which I assume the CTxx TOS probably does, and thus HB sees a cookie value it does not like and a CPU value it does not like. This is case with my Hades060, CPU cookie '60' and FPU cookie is not what one might expect.
What is baffling is why HB needs to fiddle with the FPU at all. It's merely a text editor when it comes down to it, and it should be able to spit out FPU code for a compiled app regardless of the state of the host machine it's running on. The same applies to the CPU, there is no real advantage to the TT version, the standard version should be able to spit out 030 code for your compiled app, if HB has that option, it just might process it slower.