The kind of sound you’re describing is sometimes indicative of a failed reed, one that has a fracture in it that may not be visible, Johnathon, especially if the problem is not resolved by changing the gap. It’s also possible that the reed is a little bit off center (or twisted) and is hitting the side of the opening. You can tell by springing it slightly into the opening and then out (without bending) to determine whether it’s scraping or catching on one side or the other. Another possibility would be that there’s a hair or particle of something interfering with the reed, but you’d see that when you open it up. Still, try blowing around the reed to clear out anything that might be interfering with it. You could also rinse it out with water. And make sure the reed is clean.
Try also “pinging” the reed with a toothpick or pin to see what kind of sound it makes, comparing it to the pinging of reeds around it. (There should be enough of a gap between it and the reed plate so you can do this without it going into the opening.) The ping of the E reed next to it should be identifiable as E. If the F makes a wheezy sound when pinged like this, and if there’s nothing interfering with it, that will be a clear sign that the F reed has failed, for which there is no cure.