If I understand correctly, then following may be considered:
While your process called from LabVIEW's system excec VI is in progress, can it be made to write the events or it's outputs at different stages of completion ? Process is still running, and updating the 'event tracking file' say.
Now an other program (say monitor.exe) can read this file online and display the status, while your original process is still running.
Purpose of online monitoring will be solved except that some other program is displaying realtime data for you, instead of your primary LabVIEW program which called it.