Hi Steve,
Where did you find this information? I went through Scott's but could not find it. However, I did find an answer to my question in the Afinsa specialized Portuguese catalogue and although I do not speak Portuguese, I managed to find out that there have been 2 postal reforms in the 19th century. At the time of the first one certain canceltypes were used (see fig. 1) and the cities / municipalities were assigned numbers. Funchal / Madeira had indeed nr. 51

Then in 1869 a second reform took place. New cancellers were introduced (see fig. 3) and the numbering was rearranged. Funchal/Madeira now had nr. 45.

Now have a look at my stamp. It is from 1873 (the overprint from 1874), so that is after the second reform, and frankly it does not really make much sense to me to put a fake overprint on this one, as the not overprinted stamp is worth twice as much :)

Afinsa does mention authorized reprints from 1885 and 1905 that are worth far less, but I cannot imagine these being cancelled with a number cancel that was abolished at least ten years before. Afinsa actually only values these reprints in mint condition, not used.