Overall, it's probably not going to matter no matter what you do. So I wouldn't stress about this. Although me telling you that isn't actually going to make you not stress about it.
Send three now, add a 4th later is a totally reasonable plan. You have two audition rotations coming. Remember that a letter from an audition won't help you match into that program -- they will certainly talk all about you at the program whether you submit a letter or not. So these future audition letters are for OTHER programs. if you have a rot at a very presitgious place, get that letter and then submit it to the other programs where it might have a big impact. Tell the person at your second audition that you've already submitted all your letters earlier in the season, so you'd appreciate it if they sent their impression directly to the PD via email.
If you don't get a letter later, or if you worry that your performance wasn't great at the prestigious place so you don't want to ask for a letter, then you just submit the 4th letter. No worries.