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I have 315/75R16s on my stock 2004, it does have the snowplow prep package so it sits level. The rub at full steering lock on the leaf springs and I had to cut the lower part of the front bumper as well as the lower part of the fender liner on the back of the wheel well. Long story short yes they should fit.
'04 is radically different than a 97. Just like fitting the 35X12.50s on my 07 is a different issue than putting them on an 04.
Your issues will be wheel backspacing and steering stops to stop the tires from rubbing on the leaf springs. The front bumper isn't hard to space on your year of truck if you front side the wheel well a little, but I honestly have no idea about how well they'll fit.
ttb sucks. i took it in for an alignment and they told me that they didn't know if they could adjust it but they wouldn't touch it until i replaced an upper ball joint and my pitman arm