What RPM does it rev up to from a stop? The converter stall speed should be around 2500RPM when you first nail it. I had a 4-spd 5.3 with 3.73's so probably equivalent to your 3.08 and 6-spd first gear. When you have an already low 335 ft-lb torque at 4000RPM and the converter limits it to 2500RPM, it's going to feel like a turd when you take off from a stop, especially when heat soaked. Might just be normal. You said it wakes up around 15mph which is where it starts getting in to the torque peak.
Keep in mind that your 1st gear overall ratio is comparable to the 3.73 "towing" gears of the past 4 spds so I wouldn't sweat it.