People have different ideas of joining I guess. To me it shouldn't be stressful on the horse, just let it know you're displeased. I just did it again last Sunday with my mare who has recently moved to a new facility. It was cool enough to finally check her new saddle and do some ground work. She was an angel while I was doing her groundwork, then I tied the rope halter lead up so she couldn't trip on it while she grazed, so I could take some new pics of her. Put the camera back, and went to get her and she did the amble/angle on me, LOL. I took a step toward her shoulder, she took a step away. I took a step forward she took a step forward. (The arena doesn't have a gate) after a few steps like this I ran her away from me. Like the alpha would do in a herd for bad behavior. O got my stuff in the arena and headed to the barn and she came trotting up to me but of course she wanted her saddle off, LOL so I ran her off again. She went to the fence where the herd was, on the other side, and I went there and ran her away from the herd. Now doing this you face them full on. After that time I turned sideways to let her know she could come back. And she did.
I've gotten the idea here that some people consider joining be done in a round pen or an arena and you keep the horse running, and making it change directions for a long time and when you stop the come up to you and follow you every where. I've never wanted that and never done it that way. I want her to stand still when I walk out with her halter to get her, or like in the arena that day. I don't want her following me around all the time, LOL, there's 6 in her little herd, and when I go in where they are, they all wanna follow me anyway. Anyway the type I describe can be done at a trot, and isn't stressful, just letting your horse know he doesn't want to run away from you.
Also the grooming was a great idea. When I first got my mare, she'd been abused and I used to mosey her (halter and lead around the farm eating the grass on the outside of the pastures. I always took my massage brush in my back pocket and brushed her while she ate.