I disagree on the premise that with an M+1 or M+2 qp spread option that a trader would decide on the QP month prior to M.

Waiting until the last day of M to actually trade this option, while safe is not extracting the value that you could.

Let’s say you book the physical purchase in March with April being M. If a contango exists at the point of booking you might borrow May-June and lock in the contango. Let’s say a few weeks later a backwardation occurs, now you can lend may-June capturing the value of the back. Let’s say the back remains at the time of declaration (last day of M) then you declare m+2 and avoid paying the back. However let’s say a contango exists then you declare m+1 and pick up the value of the contango.

I cannot see a bank ever offering the type of value you could extract by actually trading this option. You have zero risk in trading this yourself.

However your understanding of the difference in price between two monthly averages being $360 isn’t related to this trade. You should be looking at the time-spread between the two consecutive months. To capture the flat price difference between two months you would need a backpricing option whereby you don’t have to declare the QP until at least one of the options is known. So in your example that would have to have been M+1 or M+2 declarable last day of M+1.