Sounds to me, like you could benefit from doing some tall movements. I'll defer to others, but I think you need to start with the bar and learn to catch the bar smoothly from the tall position. There's some great instructional videos in the Resources page here.
Personally, I'm doing a ton of tall and hang movements for a different reason - I have an aversion to getting under the bar. For an intirely different reason, i think these movments would be beneficial to you in learning to not "undershoot" the bar when you're going into the third pull.
I would do them as part of your warm ups for your main movements. No need to go overboard. But you will need to teach yourself to be smooth on that third pull. Meet the bar. Don't let it topple on you.
Be patient. It will come in time.
All the best,