Out of curiosity, I did a little searching on the 99 250 RAWR. There is not a lot of actual numbers available, other than the 6,830 lbs that is in your vin. According to a early day Ford fleet, as well as a couple Ford forums, both the 250, and 350, carried the same rating of 6,830. The axles were the same, and the RAWR was determined by the OEM tires installed.
I did also see truck forum people mention the 6,080 that John found. In any case, with the 3,415 new tires on the truck, you are good for at least the 6,080. Also, if for whatever reason the REAL weight police checked you, they would just be concerned that you were within your tire weights. In some states, for what your truck paid registration is.
Jerry