Lycoming has a tech support line that might offer some help. They have always been willing to go the extra mile when I've called. Here's a link for contact info:
My immediate guess is that with the large cylinder volumes and high compression ratio, this isn't an engine that will handle auto fuel easily. I think you'll need to reduce the compression ratio for the engine to be happy on mogas over the long term.
The next question is whether they have lower compression pistons for the 390, given that it isn't a high volume item.
If you do touch base with Lycoming, it would be appreciated if you could follow-up in this thread with your findings.