Sloppiness is not normal, this is why I suggested you could need a modulator adjustment.
On part throttle, the 3 to 4th gear shift should almost be imperceptible but should not feel as "hanging' between gears.
You said: "And under load (i.e. spirited acceleration) the hanging seems more pronounced". Again, this is not normal. A stronger acceleration should produce a crisper shift, not a longer "hanging".
At least, this is how mine operates