I've seen people ask the GA before if a paid upgrade were available (at the gate) and they were placed on the "wait list." They ended up edging my SO out of an upgrade (which meant I sat in back; I don't know how this happened, to tell you the truth) and they coughed up $$ (don't know the exact amount) for a MEM-LAX flight.

So you might just ask at the gate too (and offer to pay) if an e-First upgrade doesn't come up during OL or Kisosk check-in.