If its your monthly tourney, I'd suggest playing both games simultaneously. It sounds like you're making good effort with communication. Hopefully it can be worked out. You can't make someone play faster.
According to the rules for the monthly:
3. TIME TO MOVE – Both players should communicate in advance when they will play. When both players are engaged, moves should be made within 15 minutes. If you need a long pause in the game, be courteous and notify the other player via chat. If there is no conclusion to the round during regulation time, then the aggrieved party may record the round as a loss for the other party, indicating “no show,” “forfeited,” or simply, “time ran out” as the reason.