In ambient products in a product matrix it is expected that sulphite levels will generally decline over time, as these will interact with component parts of the product (or products of other interactions in which parts of the product are present) and this is how sulphites serve a "useful" function - there is of course the microbiological preservative element, but e.g. in wine there is also a more general preservative effect, spanning everything from enzymes to oxidation events that would otherwise generate off-notes. It's fairly complex chemistry in some senses, as there is a great deal going on.
Exactly what the behaviour would be on the surface of a packaging product is not something I've seen any data on, and in any case I'd expect it to be very specific to the "product" matrix, whatever that may be - some moisture and possibly a bit of residue of the meat product?
I'd expect that temperature will also be difficult to account for, as whilst it's generally a safe assumption that most types of reaction will slow down at lower temperatures (as a lower temperature basically means there is less energy in the system), the exact effect could be expected to be dependent on the specifics of the reactions that are occurring.
You know your product and process best, but at face value I'd be reticent to rely on any depletion of sulphite content in this way as any sort of control measure, particularly over such a short timescale - consider that some products in which sulphites are supposed to provide a technological function rely on them lasting for months/years even at ambient temperatures.
I think in your position I'd start by looking at the levels on the outside of the boxes immediately after packing them, and taking that as the effective level present for the purposes of planning how to handle/control the potential risks.