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@JesperXT
Stayed in bed, sorted the work inbox, and then went hunting for a crankset. Found a Shimano RX100 fitted with a 44 tooth Sugino Messenger and some Shimano SPD-SL's. Didn't look too good, but pedals spun freely, and the teeth on the chainring weren't too worn:
Sheldons chainline guide states that Shimano double cranksets use a 43,5 mm chainline, which puts the outer at 46 mm. According to the bottom bracket size guide on the same site, the RX100 A550 crankset uses a 113 mm bottom bracket. The rear wheel has a 42 mm chainline, so I'd like to move the crankset 4 mm inwards (actually a bit more, since the Messenger chainring is 1/8"). The bottom bracket box delivered a used, but smooth 107 mm Shimano UN-54 missing a cup. Found a used plastic one that'll do. The chainline will be around 1-1,5 mm off, which I can live with...