I would be very surprised that you could make a report on an another trip that the one you booked.
particularly if you do not have any miles in their bank, I do not see any possibility other than an operational upgrade, but I do think that the coach are not full tthese days.

Try to stay in the biz toilet when taking off, and land in one of these nice seats of this class 20 minutes later (I am pretty sure this si a bad advise).

When making one of these transatlantic trip in coach the past two years, I was never upgraded to biz, besides I am Gold.

Otherwise, I do not know CO on transatlantic, Delta is OK. But on national, I would definitevly prefer CO, as far as I know (I made only a couple of flights with them).