How To Socialize A Greyhound With Other Dogs?

We’ve had our greyhound for a little over 3 months. She’s perfect with my parents dogs when we visit their house, but growls at new dogs that we meet while on walks/ in pet stores/etc.
Usually it’s a hackle raising growl at the new dog as they meet face to face. The growl happens so fast that I cannot seem to find a time to correct before she actually gets that growl out.
She seems to want to meet new dogs, but doesn’t pull us over to them. She’s very polite on the leash. I think it may be getting worse as she settles in more and more with us. Maybe guarding me? She is a momma’s girl….
After the growl happens I try to redirect her attention to stop the growl. If I physically pull her back she will try and lunge at the other dog, so I try to move to the side and get her away.
Usually if she’s off leash and with the dog in a pen or fenced in area she’s fine after a “your not the boss of me growl” I almost feel that she doesn’t know how to greet other pups in a social manner so she feels uncomfortable and growls, which puts me on edge!
It’s only with dogs that I let her meet, never at dogs we just walk by.
So I guess my question is how do I help her become more comfortable? Most dogs we meet on walks have no manners and are crazy! Not balanced polite dogs. Usually dragging their owners over to us to meet! I can certainly see how that would make our pup uncomfortable. I hesitate to take her to a community dog park and turn her free. The dogs there will probably be too excited for her to learn how to properly interact with dogs.
She’s NOT food motivated and will refuse to take any treats if she in any type of new environment. Sometimes will even refuse to take treats while we are training in our quiet apartment. I iwsh I could get her motivated enough for some clicker training.
I hesitate to sign up for a dog class, I almost feel like it would be a waste of time. She’s not in need of any help, other than socializing with a bunch of different types of dogs.
Any ideas on what I could do?