The key thing to keep in mind is 2013 was a mid-model refresh year, for the Ram. Although they look the same on the outside, there were significant changes or "upgrades" some say, which make the 2012's different from the 13's. The entire electrical system was improved. The entertainment system was much improved (although I like a regular old-school radio). The front end bumper/grille etc ....a lot of parts are different. They started using the 8-spd ZF tranny, which a lot of owners prefer. The electrical in 13's+ seem to be somewhat more 'buggy' but that might just be a feature of it being more comprehensive. Also, Electric Power Steering was added to the 1500's. There have been a good number of users who've had issues with EPS...and it's rather expensive to replace. But hard to say from forum posts how big of an issue it Really is. Anyway the point of all this is to point out that many items and sub-systems are different between 12's & 13 1500's, and which of those differences are better or worse for your unique needs?
I think the guys who recommend the 2500 for 38's make a great suggestion. It's a heavier truck, nice beefy HD front axle (1500's CV's aren't the most robust for tires that large). Sits taller too! 2500's had conventional hydraulic steering even after 2013. 2012's and below 1500's have conventional hydraulic steering too. Cheap and easy to maintain. I would factor that in if running large tires. Having the 8-spd tranny may or may not be a factor for you since you'll probably be looking to re-gear anyway. If you do your own maintenance, the Chrysler RFE's 6-spd allows the DIY owner to check the fluid via a dipstick (can't on the 8-spd). And it's a solid tranny too. OTOH, will you get the benefit of the 8-spds if you re-gear? Maybe. IDK ...I'll let someone else who's running larger tires answer that. Then you have the whole issue with the transfer case differences. That's been well documented on the site. They're both strong enough, but work in slightly different ways. Lot of youtube videos on it.
You could always buy a regular cab long box 2500 of whatever year you like, remove the box, section the frame and reweld shorter to accept a (replacement) short box. Street rodders do frame mods all day long and a short box (salvage or take-off's) should be easy to find. Maybe you'd even want to put on a Rambox. Regular cab long box trucks probably are the cheapest on the market so you could afford to stick some money in one if you got it for the right $$. Or if you like the look of a 2500 RC/LB (like I do) ..then stick with that. You can certainly haul a lot more.
One other factor often overlooked, a positive for you, is Ram regular cab trucks have more space behind the seat than most other regular cab trucks I've seen. There's a good 13" of space at the bottom and a plastic tray that'll fit gallon jugs and bags of groceries ..tools etc. A not real common dealer accessory was a cab organizer which fit behind the seats along the back of the cab. Mine doesn't have the organizer, I wish it did. What I'm saying is, since you like reg cab's you still have some storage back there ...depending on how far back you put the seat.
Sorry for writing a 'book'. Hope it helps you in your search.
Best of luck!!