No idea whether this is garbage or has already been taken into account.
In large scale orbiting systems, equivalent measurements relating to size are based on centre of masses, where the masses also govern the force controlling the orbit.
In hydrogen atoms the masses still determine the orbit, but the forces are mediated by the charges rather than by the masses directly as gravity, which may not be in the same place as the masses and may be to some extent free to move in relation to the centre of mass
Looking at this classically - which is very wrong of me - in both electronic and muonic hydrogen, the centre of charge of both the proton and the electron or muon rotate about a fixed point in much the same way as the centres of mass in a 2 body orbital system move around a fixed point between the centres of mass at distances governed by the ratios of the squares of the masses. But in the atomic system if the mass of the proton and its charge can have different centres, the mass of the proton can remain more nearly in the same place, leaving the proton's centre of charge some freedom to orbit the proton's centre of mass and placing the mass centre of the proton nearer the combined charge centre of the orbiting proton and electron or muon pair.
Given that the muon is much heavier than the electron, the orbit is smaller thus the combined charge centre of the proton muon pair will be much closer to the centre of mass of the proton. This means that the protons centre of charge always remains closer to the centre of gravity. Thus the centre of gravity of the proton is not needing to move so much in a muonic hydrogen atom
Or maybe the centres of mass and charge of a proton are separated by a fixed distance and in muonic hydrogen, the mass does not need to swing around so much to accommodate the orbit.
It would be hell to solve in classical mechanics - never mind quantum mechanics.