ACEA C3 oils are usually reserved for diesel. The best C3 oil I know of is Mobil 1 ESP 5W-30. I live in NC, and you probably in FL, so I assume you want a hair more protection for your motor. I don't have an oil cooler, so my oil temperature fluctuates with ambient temperatures, never mind that it gets up to 240~245 when towing. So I run Mobil 1 FS 0W-40 until (if ever) I install an oil cooler.
I recommend you don't worry about TBN with that oil, just run it to 5000 or 6000 miles and dump it. TBN can't be any worse than what you get from regular ILSAC oils. You also have no reason to spend money on exotic oils.
One of the best 5W-20 oils you can get for your truck is PUP 5W-30 with a realistic cSt at 100C of 9.4 ~ 9.5. Something a hair thicker than is Rotella Gas Truck 5W-30. If you want a full SAPS 5W-30 that doesn't cost you an arm and a leg, Walmart carries Castrol EDGE 5W-30 European Formula ACEA A3/B4. You will see no benefit from running ACEA C3 oils in that truck, except maybe your wallet will suffer
What's the benefit of running a full SAPS oil in that motor? More additives and more detergents. If you're towing a lot, even with a cooler, you can safely run Mobil 1 FS 0W-40 in that climate - it's the best and cheapest 5W-30 that I've found so far. Of course, you will find people saying "use what's recommended until you run out of warranty and then use what you want". That is totally up to you, however, the warranty can't be void simply because you choose a higher viscosity motor to have better protection in a hotter climate. Just don't go too far off the reservation