Every civilian male is required to contribute money annually for the purchase of public sacrifices. The sacrifices must be publicly owned, as defined by having been bought with public funds. (cf. Ra'av on Sh'kalim 1:5) The same goes for the money used to purchase the animal. The concern for the latter impingement of the efficacy of the offering gives rise to limitations on the acceptance of voluntary donations to those from donors whom we can be sure are wholeheartedly donating to the public and not retaining ownership of the money or the animal therewith purchased. (Aruch Hashulchan, Hilchos Sh'kalim 83)
The procedure for collecting the donations is described in mishna (Sh'kalim 1:3) and elsewhere as involving
tax collectors collecting sh'kalim locally - outside of Y'rushalayim/outside of Israel - or
counters set up in and outside Y'rushalayim with one-way labeled collection boxes gathering coins for particular uses in the mikdash, including public offerings. (Sh'kalim 2:1)
Obviously track was kept of who hadn't paid because the potential existed for extraction of unpaid sh'kalim by means of liens. The fact that the authorities in charge of collecting the sh'kalim wouldn't accept them from some people implies that there was some screening at the time of payment and anonymous tossing of coins into the boxes would be impossible.
How is this accounting done, given the need to know a lot about the sources of the money and at risk of invalidating one or more public offerings? I've done a fair amount of conjecturing of my own (See below.) but I am looking for a detailed description based on more than conjecture - either solidly inferential or historical and corroborating or denying my assumptions above - such that I can picture/one could execute the procedure.
E.g. Do we start with census data to tell the tax authorities who is subject, keep a written record of who reports (and authenticates) for donation, then compare them? How does that account for the screening step? Or is there no need for a screening because of an administrative corrective procedure at some point to conditionally replace/buy any money that may have come from invalid sources with valid money?