As someone that was in your shoes, it isn't the worst reason in the world to get a new truck. LOL
My 3/4 ton is really nice and the wife had a hard time arguing about buying it.
I can only speak for myself, but with the numbers you have, I doubt you will ever be happy until you get a "bigger" tow vehicle.
My 1/2 ton truck was within specs for our trailer, but after several hours of adjusting the hitch over and over again, I still wasn't happy with how it handled and then I got a 3/4 ton.
Now we are moving up to a 5er and at least I shouldn't need ANOTHER truck, with my knowledge now, will stay within the personal limits I have set for what to buy.
Good luck and have some fun with that new trailer.
2015 32 Foot Rockwood 8289WS 5th Wheel
2013 Chevy 3/4 Ton TV