Naw the cable is very easy to change - just watch the direction of the seal at the crankcase

the carb may take a little thinking

If you pull the vac line off the carb & suck on it, it should hold that vacuum.You should get no gas. I checked mine the other day & was able to pull a vacuum & plug it with my tongue & held it long enough to see that it wasnt leaking down.

A piece of tubing on the nipple under the carb bowl will let you drain the bowl into a glass container & you can see what comes out. If it's dirty I would run the bike low on gas & drain the tank into a container, pull the petcork & check the screen. It Can be done with the tank on the bike, but reinstalling the petcork is a bit fidgety. It takes a gentle touch to reinstall it & not bend the plastic tower the screen is wrapped onto. If the tank is really loaded with crud, I wouldnt know the best way to flush it.

  First try some SeaFoam in the gas it might clean it up and you want have to take it apart.

  The dirt dissolves and goes out your muffler.

I hate to sound like a simpleton after all those well-articulated comments.  But I'm going to anyway...

When you are low on fuel, climbing a hill positions the pickup tubes on the petcock in such a way that the bike will "run out" of gas sooner than expected.  Before I opened anything up, I'd eliminate that as a possibility by switching to reserve next time it happens.  

On the other hand, Savage Greg's Julie was having a similar problem, and I don't know if he ever did solve it.  It only happened in Montana, so maybe her bike just didn't like our climate.

I have mixed feelings about Sta-Bil. I have been unable to find out what it actually contains, as the MSDS I have found seems to say only something about petroleum distillates. I went for about fifteen or so years with no additives whatsoever in either gas or oil, and had no trouble whatsoever. This included, in one case, a bike that sat for a year with a full tank of fuel (although with a drained carburetor). In Nebraska the non-riding season can be long, and all bikes sat with full fuel tanks for two or three months at a time. Most did not have drained carburetors, because it wasn't easy to drain them. When the time came to start them, I turned on the fuel petcock, waited a suitable time (occupied by checking tires and so forth), and they started just as if they had been put away the day before. I will concede to having charged the batteries every couple of months with a low-current charger - not a Battery Tender because I don't own one. I have trouble imagining any additive that can reduce problems from none to some lower level.

However, the manuals on a lot of my equipment, ranging from motorcycles, lawn tractors, my boat, and my generators say Sta-Bil should be used if the fuel is to be stored for more than several weeks. Sta-Bil is the only named product in any of the manuals. The manuals for my motorcycles say, in essence, any other additive in either oil or fuel will do nothing except increase operating costs. In accordance with that advice, I have been using Sta-Bil for the last few years. The only effect I can positively notice is the color added to the fuel, and the different smell of the exhaust. I had no troubles prior to using Sta-Bil, and still have no troubles.

Just to add information, I have been using gasoline with ethanol added since the early 1980s. I usually buy fuel by price, and for many years the price of gas and gasohol see-sawed back and forth. Of late the ethanol fuels seem to be about ten cents cheaper than straight gas. I have never been able to reliably measure a difference in fuel economy in any of my vehicles between the fuels. Nor have I had any troubles which could be attributed definitely to ethanol. I do avoid ethanol in two-stroke equipment using pre-mix.