"So, only one factor repairing rigging then. The rules say that they can repair two rigging boxes, or one rigging box and "finish one other repair." Presumably this is one other type of rigging repair, such as replacing a sail or cutting away wreckage."
Up to 2 factors can be assigned to rigging repairs. Each repair phase you can repair either 1 rigging and some other repair (rudder, etc) OR 2 rigging. Rigging repair does not require more than 1 crew factor for BOTH rigging repair attempts. Additionally, damage incurred in the current game turn CANNOT be repaired until the NEXT game turn.
"This is sort of a lead-in to my question, which is: Could surplus crew be assigned to cut away downed masts, or do they have to be assigned to rigging repair?"
Cutting away downed masts is in addition to repairs; they are not considered repairs in their own right. Crew factors can be assigned as desired as long as the "1 rigging and some other repair (rudder, etc) OR 2 rigging" limit is not exceeded.
"Your explanation above using 4 crew factors in the example would seem to indicate that if you had surplus crew, you could use them for that, given that only 1 crew at a time can do rigging repair. If the answer to surplus crew is yes, then can they start hacking away the same turn that the mast falls?."
No. Since Cutting Free comes before Assign and Repair in the Rigging & Repair Phase, you cannot cut away a mast that had fallen that turn since you cannot assign crew factors to the task prior to the mast falling. You must spent one full turn (at least) with the mast over the side. (And damage incurred in the current game turn CANNOT be repaired until the NEXT game turn). Additionally, you'll rarely (if ever) have surplus crew factors (at least I've never seen it in all the playtest games).