Well, my GZ250 died on the side of the road a couple of weeks ago

After putting it all back together the bike is still having the same problem; sputtering, backfiring, and eventually dying out, and only when it's in gear. In neutral it runs much better

The strange thing is the bike ran fine for ~200 miles. I put a tank of high-grade in it, rode it about 50 miles, and then suddenly had this problem. My dad thinks the higher grade loosened some junk off of the inside of the tank which is now clogging the fuel filter.
[short story]
So I want to clean the tank out to remove any rust/varnish. My question is what is the best way to do this?
What I am planning on doing is adding a box of BB's and a half gallon of diesel and shaking it up, then cleaning the diesel out with some unleaded, then putting the unleaded back in and adding some carb cleaner for good measure. We found this method online and it sounds good.
Has anyone tried this, or another method that works well?