I do not see why you think the association with Prins Willem Maurits van Nassau-Siegen is "a bit far-fetched". Willem Maurits was Colonel of the regiment from 1673 through 1684 when Haersolte took over. In addition, one of the companies in the regiment was provided by Nassau-Siegen. The flag could be a holdover or belong to the Nassau-Siegen company.
I am not questioning the link between Willem Maurits and Haersholte, perhaps I wasn't clear on that. We are dealing here with a flag that is quartered, with the colours white, blue and a kind of red. (The Hoynck version is different from the Belaubre version in this). In the left upper corner it shows William III Dutch weaponshield topped with a Kings crown, the weapon surrounded by the motto of the order of the Garter.
There is therefore a link with William III, Stadholder of Holland, Zeeland, Utrecht, Overijssel and Gelderland. I accept therefore that the regiment was paid by one of those provinces. What I don't can't figure out is the link with Nassau-Siegen. Just the colour? In that case you can also make a link with Count Waldeck who was married to Elisabeth of Nassau Siegen.