From what Ive seen... if its sticking, it aint the reed - and it likely isnt the cork unless the cork or cork notch is huge and there is a lot of room for adjustment (like Stump said, cut er in half).
Now Im not saying that the cork or the reed arent important tuning factors, but trimming 1/8" off a reed or cork isnt likely going to cure a sticking problem - unless of course there is a huge "defect" in the sound board that makes the cork have a huge reed altering affect - something like a step or saw blade gouge or something where the cork is having a huge affect on the reed - that it shouldnt.
If you get through a few more and still fight the same issue, youre welcome to send one to me to look at... I can even tinker with it if you want and send er back with a little bit about what I did where and you can then see how it affected the call for your calling style.
That is one thing to keep in mind... I dont know your calling style, or how good a caller you are... There is a chance that maybe somewhere in there - the problem lies?
One thing is for sure, that reed is too long for the tone channel, or the tone channel is too short for the reed. And the tone channel doesnt look like its too short to me.
Oh oh oh oh .... just had a thought....

You must be using a brat point bit for your tone channels? It look s awfully squared up at the tip. Id be inclined to either take a small carving tool, and make a point on that tone channel so that it looks like it would if drilled with a normal 118° drill bit (basically lengthening the tone channel the length of the point). OR - fill the tip of the channel with JB weld or Epoxy, then reshape the tip to pointed like a drill bit. Just an idea, but I have seen some soundboards that can handle a square tipped tone channel, and some that cant...
Wade