If she’s really ring sour, then I guess the round pen is out to start (because that’s where I would start otherwise). How about starting in her pasture? Clicker training can be a great foundation for a sour horse. A safe place to introduce it is over the fence or stall door and training the horse to lower her head to get the halter on. She may already be fine to halter, but they can always get better. You can get to the point where you can just hold it up by the crownpiece and they’ll thread their nose through, so you can do it one handed. With enough practice and a stable enough bit (like a Mullen mouth) you can even do the same thing bridling, though obviously it takes 2 hands to get the noseband and throatlatch buckled.
From there, you can try the round pen. But if that’s still a no-go, take the mounting block to the pasture and practice that. You don’t have to get on, it’s more just teaching her to line up and stand still. This is another good opportunity to use R+ training and build back her curiosity and work ethic.
You can also hand walk her if she’s not too flighty and energetic. Practice walking and stopping. The idea is to get her to mirror you and focus on you. Treats still help a lot at this stage. Starting a hand grazing habit can also be more helpful than you realize. It trains her to watch your movements and learn to negotiate her body around yours, to relax in your presence, and to allow you to reorganize the lead rope or loose it if she steps on or catches it somehow. It helps to have a 6ft lead and an area where it wouldn’t be a big deal if she had a spook and you needed to drop the line and let her have a little bolt (ie, not near a road, or where lessons are going on). You don’t want to have to restrain her if she spooks; what happens is they don’t go very far and often either come right back or stand to let you grab the rope again, and eventually they learn to “spook in place” because they realize they feel more secure being attached to you.
Once you have a good rapport and the horse is less sour, I would start in the round pen. If the horse is really energetic, you might want to start with free lunging. But there are pros and cons to it. Some horses can work themselves up into a panic and get very insecure at liberty. If you have them on a line, you can reel them back in and talk them off the fight-or-flight ledge. But a pro of free lunging is that you’re not restraining them, so you’re not fighting with them, and it gives them the choice to turn away from a blind panic (or even just a nervous trot with a counter bend) to put their focus on your direction and start using the thinking side of their brains. Either way, the first step in the line or at liberty is asking for a lot of direction changes. Doesn’t matter what gait at first, just get a lot of direction changes and gradually you will get your horse’s focus and relaxation will follow. I think Tristan Tucker’s method is similar in principle but a little harder to follow, especially with a hot bear that wants to run. But the basic principle is getting them to move their feet and shoulders in response to your body language. As they move their feet, their brains seem to settle.
Once your horse is calm and focused on you in the round pen, you can start lunging. Try to train all your transitions on voice commands. Transitions can be just as good as direction changes for getting your horse’s focus. After a month or so, when your horse is going calmly at all 3 gaits, it would be great to get a system like the pessoa, but even just lunging in a neck stretcher attached to a surcingle will help teach her about contact. Double lunging is another option—even better and more like a rider—but it requires more from you. I would start with a gadget first and then progress to double lunging.
Do that for a month or two, maybe three if you are being conservative, and I bet anything your first ride will be nothing like your last one. You’ll have a different horse!