What changes when you fly slow onto a short strip, and how to handle it from a desk where you cannot feel the sink coming.
The more I pulled to stretch the approach, the more the aeroplane sank
Below best-glide speed, and unambiguously so as you approach minimum-power speed, the usual relationship between pitch and flight path inverts. Pull the nose up and induced drag rises faster than lift; the aeroplane slows and sinks more, not less. At STOL approach speeds you are living in this regime, which means the controls swap jobs: power controls your descent rate, pitch controls your speed. Once you fly the approach with the throttle instead, the aim point stops wandering.
I keep greasing it on, but the aeroplane won't stop before the end of the strip
A greased-on landing means the wing is still flying, the wheels are barely loaded, and the brakes have almost nothing to work with. The sub-100-feet-per-minute "butter" the community celebrates is, at a short strip, a description of failure. A deliberate, firm arrival on the main wheels at minimum speed puts weight on the tyres immediately, kills lift, and starts the braking phase now. What matters is where and how slow, not how soft.
Holding the stick fully back through the soft-field roll is exhausting and my pitch control wobbles
On a spring-centred desktop stick, holding full deflection is tiring and imprecise, and half-deflection creep is invisible. The desk workaround, which would be poor technique in a real aeroplane, is to trim fully or nearly fully nose-up before starting the roll and let the trim hold the elevator for you, feeding in stick only for fine control. More generally, trim is your substitute for feel everywhere in slow flight: trim for the approach speed and the aeroplane will tell you about speed changes by moving away from the trimmed attitude, which is a cue you can see even though you cannot feel it.
I never see the sink developing until I've already hit the ground hard
The vestibular system announces a developing sink rate immediately; a desk pilot gets it visually or from the VSI, a second or more later. On the back side of the power curve, a second is a lot. Until your eye learns the visual signature of developing sink (the aim point sliding up the windscreen), fly your STOL approaches two or three knots faster than the real-world technique would prescribe. You will give back a little float; you will stop arriving in unrecovered sink.
At a mountain strip the takeoff roll used nearly the whole runway
The rule of thumb for normally aspirated pistons is roughly 10 per cent more takeoff roll per 1,000 feet of density altitude, so a 5,000-foot-elevation strip on a hot afternoon behaves like a strip half its published length. This is also where the widely taught 50 per cent margin earns its keep: take the POH landing or takeoff distance for the conditions, add half, and if the strip is shorter than that, the answer is no.
I pulled the power in the flare and the runway just came up at me
You chopped power in a slow, draggy configuration and the sink rate spiked instantly, because on the back side of the power curve, power was the only thing holding the descent rate down. At STOL approach speeds you are living in this regime, which means the controls swap jobs: power controls your descent rate, pitch controls your speed.
I overshot the turn onto short final, fed in rudder to tighten it, and the wing nearly let go
The classic bush killer, named for the real-world habit of circling low over something interesting: overshoot the turn to a short final at low speed, feed in inside rudder to tighten the turn without steepening the bank, and skid into a stall-spin with no altitude to recover. At 400 feet this is unrecoverable and no real instructor can safely demonstrate it. At a desk it costs nothing, which makes it a mandatory exercise rather than a warning: set up the overshooting base-to-final deliberately, first at altitude, then at pattern height, and learn what the skid looks and sounds like before the wing lets go.