I'm very new to poly, and as GG knows, very new to this forum. But one thing I can say, from the position of a person who struggles more than her poly partner, is to be extra careful during this time.
If you can stand it, keep working with him. I won't speak for timing, or whether that work will pay off for your end goal. Others here will give you excellent input on that.
Just know that any slip ups, in his stage in the process, could be detrimental to your cause. Like, if you see the person of interest and fib about it, or try to develop a further relationship without telling your partner because you don't think you can help it... that would take you many, many steps back.
Are you in danger of acting on your feelings? Or can you have patience with your man to understand your needs? how long have you been together? How long are you willing to work with him? Is this something you can wait 6 months for, while he learns (assuming he agrees to learn)? Or even a year for? Or is it more urgent than that?
Could it be that part of his reluctance is because this is a close friend? I've had experiences where dating too close to the social circle can really cause more problems. But I've also found comfort and success in dating someone my partner knows and likes. It can go either way.
Is the third party open to poly/being a secondary or other significant other (OSO)? I wonder if they could start the conversation between themselves more comfortably? Or with you? If it all works out in the future, they should have some communication, why not start now?
Again, am no expert, just my two cents.
Hang in there!