That's still a lot of turns. Did you run this system in the last game you mentioned?
If the fighters aren't going to level up or have different stats then it's basically a drawn out coin flip. I'd recommend starting with how many rounds you want combat to last, then having each player roll a die. Keep a cumulative total running, and at the end of the last round the highest total wins. The difference between the totals can be interpreted as how badly one side is winning/losing. If you want to spice it up from there, you can make a 1 or a 20 end the fight immediately. The number of rounds could be more/less depending on the importance of the fight. Maybe 3-5.