I have a 2005 Dmax, CC, short bed, so pretty similar to your truck, also mildly programmed with a Hypertech programmer. We tow a 36' fiver weighing in at around 12K loaded. I am just a little over the truck's GVWR, but well under the RAWR, especially since I'm running load range E tires with about 1400 combined lbs more capacity than stock, although even with stock tires I'd still be within RAWR. I don't have air bags... though that may help even more with handling and chucking. If you have old shocks, I would replace them. I replaced mine with Bilstein 5100 blue/silver shocks, and it made a huge difference in ride while pulling.
I have no issues with handling, or hills, up or down, even here in the California hills. The Allison does a great job of keeping steep downhills tame with very little need for tapping the brakes if at all. The truck feels and pulls great with this load. I have no idea about heavier.