My 2-155 is doing about the same thing, except it shifts easier when you first start it, but then gets worse. I'm betting that my pilot bearing is/has set up, and so the input shaft is spinning on the inside of the non-tunring pilot bearing. I have seen quite a few input shafts where this had happened, and the surface where the bearing rides gets ground down. We would take them to a machine shop and have them welded up, and turned back down, and it seemed to work good.

I'm going to guess that you have a similar problem going on. Whatever it is, it is definitely the clutch. It's job is to provide a way to disconnect the engine power from the transmission. So if the tranny is still spinning, the clutch isn't doing its job. 

It could be the throw-out bearing. If it is, you should be able to hear some gridning or clattering in the clutch area, especially when the pedal is pressed on. 

Also, check your clutch pedal free play. Too much and the clutch might not fully release. This is the simplest check to do, and should be done first.