I have received a resolution to this issue. These are the steps:
Go into Keychain
Choose Login (make sure the padlock is unlocked)
Choose All Items under Category
Search for the JPAS certs under Identity Preference (or DISS or SWFT - whatever you are having issues with - I had issues with all 3) and delete those certificates (the ones with identity preference noted)
Close the Keychain
Clear All History in Safari
Close Safari and then reopen
Go back to the site - it will take a little time to load. If it won't allow you to proceed due to privacy issues, go back to Keychain and search for the certificates. Under Trust, make sure Always Trust is chosen. Clear History in Safari again, open and close the browser and it should work when you go back to the site.
This process has worked for me to access JPAS, DISS and SWFT. The only problem I am still having is accessing NISS via NCAISS, but that's a different Help Desk, so I'm hoping to reach someone who understands Macs there as well.