Kind of an answer:

Airtable now supports a duration field type, supporting a number of formats — or, rather, precisions: h:mm, h:mm:ss, h:mm:ss.s, h:mm:ss.ss, h:mm:ss.sss. (Unfortunately, a value entered as h.mm:ss is interpreted as ss.s, so you’ll need to import your values as a string and then convert them by replacing decimal points with colons.)

Internally, durations appear to be stored in seconds, so to arrive at a value in minutes, all you need do is configure a formula field with the formula {Duration}/60.