It wasn't Mohammed who founded Islam.

[Mudhammam]

It really is hard to explain why early "muslim" conquerors would have issued coins with crosses on them. Yet, they exist.

Not really so sure I'd agree. This explanation seems perfectly reasonable:

After the Muslims defeated the armies of Byzantine and Sassanian empires, there came the need to administer the conquered territories. The early Muslim from Arabia did not have a sophisticated system like that of the two defeated empires. So, the best recourse for them was to maintain the existing administrative systems just like other conquerers before and after them did. However, the early Muslims inherited two different administrative systems from the conquered two empires. Hence they had to maintain two parallel administrative systems one in the east and another in the west, which differed in their languages, culture, monetary systems and controls. The Muslims maintained these parallel systems for over 50 years until the reforms of the Umayyad caliph ʿAbd al-Malik.
Before the reforms of ʿAbd al-Malik, the Muslims used the existing monetary systems of their Sassanian and the Byzantine predecessors. There is a debate concerning the earliest coinage and their dating. Some argue that Muslims started striking coinage almost immediately as they did in the former Sassanian domain. Other argue that the Muslims did not strike coins in the former Byzantine realms until the reign of ʿAbd al-Malik. However, the middle ground appears to be more appropriate as the the coinage of the era before the advent of ʿAbd al-Malik was very complex. At some point in time, both in the east and in the west, the Islamic empire started to make its presence known via the coins that circulated in their domains. Initially, the changes were very minor with the addition of short phrases in Arabic and/or the addition of hijra dates. These lasted until a complete reform of the administrative system by ʿAbd al-Malik who united it in Arabic and changed the coinage drastically to what we essentially call as Islamic coins. The reformed coinage of ʿAbd al-Malik was different from its earlier predecessors in epigraphy as well as religious content. The new coins asserted the oneness of Allah and Muḥammad as His last Messenger.

http://www.islamic-awareness.org/History/Islam/Coins/