Communion by intinction is allowed, but only if the priest does the intinction. This means that the communicant receives on the tongue. It is really only feasible with the proper vessels designed for the purpose (it looks a bit like a cup in a large saucer).
In the situation the OP describes, the priest wouldn’t have enough hands to hold the ciborium and the chalice, and dip the host and offer it without dripping.
If there isn’t an EMHC (or another ordinary minister) to offer the cup, communion should only be offered under one species. The priest could have picked someone to help me for just that Mass. He could have offered both to each communicant, but one at a time. (Distribute the host, put the ciborium down, offer the cup, etc).
If for some reason he had consecrated a large amount of wine, he could have asked some to receive just the blood. Or he (I think) could have asked a few to help him finish what was in the chalice at the end of Mass.