So, from your last post, it sounded like you may have already been cleaning this particular rifle with multiple jags. Is that right? So there is a step or shoulder going into the recess in the breach plug? How are you getting the small jag to clear the step so as to enter the breach plug? Or do you just wiggle it around until it goes in? If you have a small jag that seems to work adequately, then is that the diameter you need? It would still be good to know the length of that small section on the factory-made jags.
If you don't yet know that diameter (and if you don't get a reply regarding measurements), then you might try sanding a taper on a Poplar dowel from Lowes or Home Depot and then pressing it into that stepped recess, so as to get a print on the wood, which you could then measure for diameter. I wouldn't want to drive it in, as it might get stuck and break off, then you'd have to pull the breach plug. But just pressing it in firmly by hand might be enough to make dents in the taper on the dowel. My thought is that if you knew the diameter, then you could have a means of estimating the size of jag you needed for cleaning the breach plug. The jag would of course need to be smaller than the diameter, but I'm sure there is a chart (or advice from someone on here) that would give you an estimate of jag size in relation to caliber/diameter.
If the dowel had a really pointy tip, then careful experiments might give you a way to measure both diameter at the shoulder and also the depth you need from the shoulder to the bottom of that chamber.
You could, of course, pull the plug. But on some types of complex breach plugs that's not advisable. Can be a bit difficult to get everything lined up again.
Anyway, I hope someone replies. My suggestions may not be that helpful. Just thinking out loud here while I drink my coffee. Sorry that my post is so long. I type as fast as I can talk.