Take a look again at the omega catalog. If they don't have a signal conditioner that will take the current range you need, they will have one with a mV input that you can use with an appropriate current shunt.
If you can't tolerate the current shunt, then use an active hall effect current transducer (essentially a current transformer for DC) and then put a suitable burden resistor on the output of that, and use the mV conditioner to convert the voltage across that resistor to your 4-20mA output.
_Or_ if you can tolerate homebrew, it is pretty trivial to use an active hall effect current transducer and an op-amp or 2 to provide the 4-20 mA output.
-Jon