I suppose they could in part, in theory, As the output of H & W was only 32 & 74 tons respectively for 1860 and H's only totalled 41 tons including 1861 coins, this implies the only possible Heaton coin is the penny with 40/40. Watts could have possibly numbered things, but as Dyer points out, this would fail based on a total tonnage of 1720 up to 1863. It is therefore reasonable to assume that all the numbered coins are from the RM.
Thinking out loud, the repeated use of the same number at the beginning might relate to production milestones such as an internal job requiring 40 tons as opposed to the full commission, or testing dies/blanks? It is also possible that the inconsistency seen for 1860-1 compared to latter figures was a mistake by someone at the mint! It is not easy to see why there would be 2 identical numbers unless for the above reason.
Anyway, it's all speculation in the absence of evidence.