You should know that the "tow rating" is a marketing term. It's never the rate-limiting step for towing. It's always payload. They suck you in with these high "tow rating" numbers, but you max out the payload far sooner.
Here is a good towing calculator.
This is a good video to watch on towing and payload. (probably should have watched this before you bought)
It looks like you've got a Coachmen Catalina Summit Series 7. The max loaded weight is 4310 lb.
You've probably got about 500 lb tongue weight, even just going with your 3300 lb figure. You don't want to exceed 80% of your payload. Yours is 1500 lb. So that leaves you 700 lb for you, your cargo, your passengers, your coffee in the Yeti mug, your floor mats (yes, those count towards your payload too), the dog, the beer cooler, etc.
I think you're over payload, and you have bigger problems than which oil to buy. I think you didn't buy enough truck for that trailer. You can confirm with a scale (pull onto it with everything you're going to tow and leave the trailer off). Check that figure against the weight in your driver's side door jamb. I'd wager you're over it.
So technically you might be able to tow 4000 lb, but only if you're a 110 lb woman driving naked without floor mats and literally nothing in the cab or bed of the truck.