How about riding with no stirrups to learn balance and help with perching?

Riding without stirrups is one of the oldest and most effective training tools in horsemanship, and there's a reason every serious riding program from western performance to dressage to hunt seat uses it. When you take the stirrups away, you eliminate the rider's ability to stand up, grip down, or brace against anything. The only option left is to follow the motion of the horse with your seat and legs — which is exactly what a correct position requires. It's uncomfortable at first, sometimes brutally so, but the results it produces are hard to replicate any other way. For perching specifically, no-stirrup work is one of the most direct fixes available. Without stirrups to stand in, the forward lean becomes immediately unstable and the rider is forced to sit back and down to find their balance. The seat bones make contact with the saddle in a way they never do when the rider is bracing in the irons, and that contact — that feel of actually sitting on the horse rather than hovering above him — is something riders often describe as a revelation the first time they genuinely experience it. Start with the walk until you're comfortable, then move to the trot, then the lope. Don't rush the progression. Ten minutes of quality no-stirrup work at the walk is more valuable than two minutes of bouncing around at the lope while gripping for survival. Build the stability slowly and intentionally. Your hip flexors and inner thighs will be sore the first few sessions — that soreness tells you exactly which muscles were not doing their job before. Do this consistently — a few minutes every ride — and within weeks your default position will have shifted. The seat that felt foreign and unstable becomes the one that feels solid, and the perch that used to feel safe will start to feel exactly as precarious as it always was.