Have you talked to the software developer for PAST? Perhaps there is an update available for download or they can create one if the understand the importance of that software to your work (and may not realize that Catalina has rendered their software useless on updated Macs, which I would think is a relatively big chunk of their consumer base). I'm not familiar with PAST software so cannot make any recommendations for alternates or work-arounds.
I found the workaround... just had to install a previous version of macOS (I installed High Sierra) in a partition in an external hard drive. I installed only PAST (and a couple of other 32-bit programs) there. Then I can boot from the external partition when I need it. Runs fine!