Grr. Just lost my comment which had all the answers.I haven't played for nearly twenty years. But I recall enough to ask whether it's the key that's sticking, ie the hinge, or the pad that it operates? Is the clarinet new? Older pads can get gummed up and so shaped to their landing zone that they get sticky...couldn't hurt to try cleaning the pad with a damp cloth. If it's the key itself, WD40? Dunno. Other than that, seems like great progress!
Get a piece of clean paper and place it under the sticking key. Press the key down and while down drag the paper out. Do this a few times if necessary. That will clean the offending key and it won't stick any more.Little tip...keys stick because they are dirty. Always best to clean your teeth before playing or at least rinse your mouth out, especially if you have been eating monte carlos before playing.
Cigarette papers are also good in the same way that Meredith suggests paper. If it's the key, do you have a polishing cloth? On a second-hand clarinet I owned, we had to get the pads replaced because they were so far gone.
Sounds good, by the way. What size reed are you using?
I'm using a 1.5 reed.It's the key. One of those funny verticle ones. Kind of seems like it's too close too its neighbour. I'll try to clean it... and to stop eating lollies while I play. It's a school instrument. Far from new. Pads seem okay.