So you have to decide up front whether you want the right answer, or the answer you want to hear. The right answer often times eliminates the truck if you don't have enough truck. I hate to tell you, but if you want to stay within all your numbers and keep the 1500, look for a smaller/lighter trailer. Unless you can create a full list of every item you plan to load up with its weight, you can't figure it out. This is why it's important to use GVWR. You don't have to know the exact number.
From 20 years experience towing heavy trailers, you will rarely (if ever) be under the numbers that you think you are right out of the gate. I've seen a lot of folks bite off too much up front and have a miserable tow experience and ultimately sell the trailer and get out of the hobby because it was too much work. If you size everything appropriately and leave some headroom, it's quite enjoyable.
7,600 x 15% = 1,140 lbs.
WDH = 70 lbs (estimated)
2 passengers @ 175 lbs ea = 350 lbs
Total = 1,560 lbs.
If you crank down the WDH, you can sometimes shift roughly 10-15% of the weight back onto the trailer axle. If you can do that, your tongue weight will drop back to 1,326 lbs. But you'll have to rely heavily on the WDH to always function. You wouldn't want to tow without it.
This is before you add anything else to the truck and assumes you'll keep the bed empty. This is about as real as it gets.
If your Ram has a Class IV hitch on it, it's maximum weight rating is 1,250 lbs.