Super, thank you for the additional information.
Since we seem to be solid mechanically in the engine, the next area to check would be the carburetion. It sounds like there is a problem with the high speed circuit in the carb. I think you have the WRIII GP with the 701cc single carb engine. If so, it makes the job very easy. You will need to take the carb off and take it apart and inspect the internals. The main thing I would be looking for is where the high speed screw is set right now and if there is some debris in the high speed jet.
Here is a diagram of the carb:
The high speed screw is reference #13. You have a high speed screw and a low speed screw. The high speed screw is the one that is NOT on the same side as the throttle cable. It is also physically higher up on the carb than the low speed screw. I want you to take the carb off first, then look at that screw and count how many turns it takes for you to turn it in until it is lightly seated (stops turning freely). Don't force it. When it stops, you stop. Let me know how many turns it was out.
Next, you need to take the steel plate (#31) off the carb and the diaphragm (#30) to get to the jets. You will also have to remove the "Body 1" to get to the jets. If you have an impact driver with a #2 phillips bit, I would suggest using that to break those 2 screws loose that hold Body 1 to the main carb body. They are usually very tight, especially if they have not been out in a very long time. Once you get Body 1 off, the 2 jets, high speed and low speed, are screwed into the main carb body underneath it. The high speed jet has a much larger orifice than the slow speed jet. #16 is the high speed jet. You will notice it is about in line with the high speed screw too. Take that out, being careful to not strip the screwdriver slot. Make sure you use a lot of down force into the jet on your screw driver so it doesn't slip. If you damage the slot and round it off, you are going to have a really hard time getting the jet out. Since it is idling fine, I would not even bother with any of the slow speed stuff.
While you have the diaphragm off, check to make sure they are no perforations in it too. Also, there is a small clear strip of mylar on the backside of Body 1. Take a look at it and make sure it is laying flat against the Body 1 as well. You can remove the high speed screw now and blow through the passage with contact cleaner and compressed air to make sure it is not restricted. If everything seems to be in order on this side of the carb, we will need to jump over to the other side to inspect the fuel pump assembly.
Again, use an impact driver to remove the 4 screws at the corners of the fuel pump. These screws are tight and tend to get stuck when they have been installed for a long time. Take the outer aluminum piece off the carb. The clear mylar diaphragm will probably stay stuck to the paper gasket which stays stuck to the outer cover. That is ok. Just take a very close look at it and make sure there are no perforations in it. Look very closely, you don't want to miss one. Also, notice is there is water between the mylar and the aluminum. Hopefully not, but check just in case.
Once you check that out, pull the aluminum block out, Body 2 (#39) and inspect the 2 small round mylar check valves that are installed on the block, on opposite sides. Mainly what you are looking for on these is a ripple or crease in the outer edge that would prevent them from sealing completely. Normally they lay perfectly flat against the body 2, but when damaged, they get that crease in them and no longer seal all the way around. If it is not perfectly flat, it will need to be replaced.
Check all that out and let me know what you find.