The IOP (PS1 processor used for I/O), SPU2 (sound processor), IPU (mpeg decoding), EE (main CPU), VU0, VU1, DMA controller and finally the GS (GPU) run asynchronously. It's naive for others to think perfect cycle accuracy for this machine might be possible with any hardware that exists today. PCSX2 is lucky to have VU1 on it's own thread. It still doesn't work perfectly IIRC, VU0 -> VU1 access is a little sketchy with it enabled.
Fixing this bug would be part of fixing a bunch of other floating point bugs, more specifically rounding and clamping.
Yes, software floating point would be slower, but the general solution would probably follow the PS4s PS2 emulator. Where each game can have whitelisted sections of code for the software floating point path.