The key is that I'm trying to develop a generic controller. That's why I must be prepared to work with any values
If you can design a PID that is accurate to better than 1/64000, you can use fixed point 24 or 32 bit routines (widely published, including here). You WILL lose anyhow trying to develop a "generic controller". What will work is to develop a 'template program' which you modify to adapt to the actual case.
Again, working with fixed point is a breeze, you only have to sequence the multiplys and divides to keep reasonable values at all stages.

Erik