If I understand...you want to continue seeing him but also find a primary? But you don't have time to date and meetups cause anxiety?
It seems to me you're giving a somewhat impossible situation: tell me how to find a primary when I'm not going to date or go to meetups. Well--I'm not sure there is a way, barring the perfect man turning up at your job.
If you want to find someone and feel you don't have time -- make time.
Where is that time going now? To spending time with a man who does not want to be your primary? If you see him 6 nights a week, give 3 or even 5 of those nights to dating men off a dating site. If you see him 2 nights a week, give 1 or 2 of those nights to meeting other men off a dating site--or to joining any sort of interest you have -- dance, poetry, music, some political interest?
Anxiety? Okay, get on some meds, talk to a counselor, join smaller groups, join an activity you love that doesn't require so much social interaction--knitting, book club, writing group, community theater or music, photo club, dance, ANYTHING.
A major reason I broke up with my poly BF was that I understood he had no intention/could not be a real support and true life companion and I knew I was unlikely to let my heart go with anyone else as long as I was with him. Moreover, I knew that very few men were going to be open to becoming my 'primary' while I continued to see someone else. This is simply a fact of life. Do with that as you will.
For the record, I am now very happily married to someone else. It wasn't easy to let go of someone I loved, who loved me, but the life he was offering me was one of being second, being forever on my own whenever the rubber hit the road.