K301 runs rough at half throttle
 

I have a 1250 with a k301 which starts fine and runs fine at full throttle, but if I throttle down, things are ok until I get below half when it starts running really rough.

I notice the same as the engine shuts down, it gets really rough and the tractor shakes. I replaced the spark plug which was dry but black, and used the gap mentioned in the manual of 0.035 though I have heard others suggest smaller gaps.

Regardless the roughness at low throttle did not change. Any suggestions? Would this point to an issue with the carburetor or maybe electrical (points, condenser, timing...)

I have not had this tractor for long so and it has always run this way since I've had it.

Sounds more like carb issue than an ignition issue to me. I'd suggest checking your carb settings.

sure your motor mounts just aren't worn out.

The K241 in my 100 with a Kohler #26 carb acts similar to this. I found the bottom of my high speed main needle is badly damaged which would lead me to believe that the main jet/nozzle is damaged as well. The assumption is that a PO tightened the needle too tight at some point.

I second this.

no, that wouldn't be a problem. it wouldn't affect the vacuum signal . I even drill those tubes out to get more fuel through them.

It was the carb settings
 

So it was the carburetor settings. Both the idle speed and idle mixture
settings were off. I gently bottomed out the idle mixture screw, then backed
it out 2 1/2 turns, started the engine and let it warm up. Once it warmed
up I started to lower the throttle and it got past 1/2 way, but seemed like it
wanted to stall. I had gotten a cheap optical tachometer and used that
to check the drive shaft speed and it was way under the 1200 RPM that
the K301 service manual recommended, so I adjusted the idle speed screw
until I had 1200 RPM and everything now runs well.

Now I'm just left with normal rattles that I will go through and tighten up or
deaden (the front bezel, where headlights would go if I had headlights, and
the hood). But the whole tractor no longer shakes and I can run it at a smooth idle. I will also have to check the motor mounts later on once I
take off the mower deck in the fall.

Thanks to all of you who responded. Probably this fall I will take off the
carb and rebuild it, but for the summer things seem to be running well
enough. I have a bit to learn about these tractors, but it makes for a
fun hobby.