Does anyone know how to upgrade the CDT definition in inflight instances?

It will not allow you to change or update the CDT type however you can create a new variable in monitor mode and make use of that variable.

To upgrade the CDT definition in inflight instances you can use process upgrade smart service. It will upgrade the CDT of all the given inflight instances to newer one.

For more info please refer this documentation page:

https://docs.appian.com/suite/help/17.4/Process_Upgrade.html

Adding to Ravi's comment you can create a variable of that CDT type but you will have to make sure that newly created variable is used everywhere to avoid further issues.

I have attempted the Upgrade Process smart service but it returns an error INCOMPATIBLE_PVS. Should I be using Upgrade Processes V2 or Upgrade Processes from Version V2?

Target model must contain all PVs present in the source model, matched by Name (case insensitive), Type, and Multiplicity settings.
For example, if the target model has a PV (`pv!person`) of type Employee^2 and the source model has the same PV but of type Employee, the process will not upgrade because the CDT types are different.

Another approach is, edit the process instance and add a newly created process (of itself) as sub-process and next node of this sub-process should reach to end nod. It will automatically take the latest one. If you need to roll back or delete any data transaction then modify instance accordingly. Thanks

You can always restart the process if possible.
If you have been keeping your processes small, you can simply go back to the parent process and call the child process again. You will then need to terminate the old child process, but the new process will contain the updated CDT definition.

Thank you all for your responses. Due to the number of inflights a compromise was reached with the affected users so that code changes were all that was required.

If you are designing a new process, make sure it is short lived. Performing process upgrades is tedious and error prone. It is exactly for this reason that Appian recommends to keep your processes short lived. Instead of tracking the progress in a process, track it using a record and related action approach. No more process upgrades!