The other option would have been to tack to starboard as soon as you realized it was going to be a close crossing situation. By tacking early, you would have given yourself clear air and the opportunity to play the shifts. In this particular case, since the wind went left, tacking early would have given you the advantage since you would have been farther left than your opponent.
It sounds like you may have been trying to get out to the starboard layline too early. In monohull racing, you're often better staying away from the laylines for as long as possible in order to be able to take advantage of wind shifts.

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