Is it possible to make an IGBT to work at duty cycles up to 100%?
Provided you respect its safe operating area and thermal limitations, the IGBT itself will have no trouble with 100% duty cycle.

The gate driver will need some attention. Some types of gate drive circuits or ICs aren't going to be compatible with 100% duty cycle, e.g. those using gate drive transformers or certain types of "bootstrap" power supply. But building or selecting a suitable gate driver for 100% duty operation is not inherently a difficult task, and you were right to make it easier by putting the IGBT on the low side of the load.