I really think a DEN stopover is the best option. DEN - JFK only has 1 non-stop and its similar timing as the ABQ - JFK flight. The rest of the DEN - NYC flights (all 2 other flights!) include a transfer in BOS. I think they can operate a JFK - DEN - ABQ - DEN - JFK or even a JFK - ABQ - DEN - ABQ - JFK route with better timing than the current ABQ flight. Since there is no plane change, you don't need to worry about missed connections.

I know it's all wishful thinking, but I'll fly Jetblue over Southwest or AA any day and those are really the only decent NYC flight options.