Re: Need help to ID and value an older rifle
The concentric circles marking is not on the side of the rifle but, as the paragraph says, on the top of the receiver ring, substituting for the chrysanthemum indicating Imperial property. There has been much speculation as to the use of the concentric circles instead of the "mum" but the indication is that the rifles were marked/re-marked to indicate use by some organization not considered servants of the Emperor (as soldiers were). Among the possibilities were those you mention as well as military academies. One source says that the highest numbers seen were 621 (Kokura) and 2598 (Nagoya), so that would rule out any large organization.
But your rifle is not one of those. The mark on the side of yours appears to be the normal Nagoya arsenal mark. The series symbol (posibly "ri") appears to have been partly obliterated when the receiver was polished at some point. In any case the rifle is very late wartime, though the term "last ditch" is rather widely misused.
It would not seem to be exceptional in that many thousands identical rifles were made, but Japanese rifles are only now being considered as "legitimate" collectors' items.