The traditional Bulgarian split squat can help you identify functional weak links in single leg stance. Improving it takes motor control to create internal stability in the bottom position, which tends to be the most unstable. And the best way to improve your stability there is by adding an isometric pause at the bottom of each rep, then exploding out of the hole from that dead-stop position.
You're going to have to use less weight, but don't worry. By increasing total time under tension to around 25-40 seconds per set, you can train yourself to repeatedly produce power in a more metabolically stressful environment while keeping movement patterns and muscular targeting on point.
Do 6-10 reps per leg for 2-5 sets. If you can't move explosively under control, then lighten the load until you can. Gradually add weight over time if you're planning to go heavy.