@Bazyle, sorry, I should have been clearer, the allen screw is the one circled:

@DC31k, it’s stationary, in the sleeve that encloses the wheel shaft – it doesn’t shift under (gentle) attempts to turn it with a bit of rod. As you say, dismantling might be necessary, though I was hoping to avoid that, since it works really nicely as is, with no perceptible backlash.
It might be that slackening the allen screw allows it to move freely; I’ve ordered an allen key – it’s 4.5mm and despite having dozens of the things, that is, of course, the only size not present.