Back to the OP's predicament: if it hasn't been sorted out already, wouldn't a wait-list request for "D" on the JFK-MIA sector do the trick? Sure, it's insane that it can't be booked in one call, but to get the seat desired on the flight in question, asking (via the wait-list) should be the surest fire way to communicate the request to the revenue management team/algorithm.

This said: I also fondly recall the flexibility that paper tickets allowed. The distinction between ticket and reservation was much clearer back then, and I'd often have the bulk of my ticket initially issued as OPEN, simply calling the operating (or marketing) airline and creating a new PNR to hold the reservation of the flights I'd wanted to take next. As long as I provided the ticket-number for them to note along with the reservation request, this was never a problem. I'd sometimes have to have the paper ticket "stickered" to reflect the reserved flight, but often, the OPEN ticket was simply uplifted as-is. Ah - the halcyon days.