I agree it is difficult to learn to feel what a horse's legs are doing underneath you. Do lots and lots of practice loping in a straight line (I think it is easier to feel when you are traveling straight). Allow your hips to sway with your horse's movement, and pay attention to how the horse's body is moving. For a left lead, you'll feel your hips move from the back right to the front left at a slight angle. Because the horse's hind right leg hits the ground first, followed by both the hind left and front right, and then lastly the front left. And of course, the opposite will occur for a right lead.
If a horse cross-fires on the left lead (let's say) your hips are going to start on the back left, swerve to the right, and then back to the left again. Because the horse is incorrectly starting on the left hind, using both right legs on the ground at the same time, and then ending on the left front. It creates a jarring rough motion. If you've taught yourself what a good lead should feel like, then you'll feel it when they crossfire.
I watched your video again and you sent her to that first barrel while she was already cross-firing. Do a few circles before you start your pattern if you need to to get her on that correct lead. If you can't correct it, don't sent her to the barrel.
Yes, this is a different manner for a finished horse. You don't have to ask them for a lead because they know they need to switch. But Squiggy isn't finished, so we have to help her as much as we can.
99% of my riding is alone riding too. Hence why I taught myself to feel leads because I didn't have anyone on the ground to help me figure it out. But it takes time and you really have to "listen" to where you horse's feet are falling on the ground.