Thanks for the DMR information. So it sounds like slow and deliberate.
Let's face it. There's a lot of things that can be done to improve the rifle and the shooter. A barrel is only one of them. In terms of the shooter to rifle interface a lighter and sharper trigger counts for much to allow the shot to be sent with as little disturbance as possible. That's got to be worth a good amount right there. I'd say it's a toss up which to do first, barrel or trigger. But a nasty trigger might mask any improvement from the barrel swap. Unless the original was really bad at least. But a good trigger might just make a decent stock barrel show it's worth if the group manages to shrink due to the shooter being able to exert less off balanced force on the gun at the point of the break.
At least that sums up what I seem to have found so far. I've got a long way to go though so feel free to correct me if that's hogwash.
To me I find that a lot of folks try to "buy performance" when what they really need to spend is time instead of money. Time at the range in practicing their rifle skills and testing of ammo to find the onee that work best with their gun. If a shooter is honest with themself and checks their ego at the gate I believe that they'll know when they have hit their limit and if the rifle has more to offer or if it's time to upgrade a barrel or whatever.
So all in all I'm thinking that if you don't have one in the gun yet that doing the very well documented mod to the stock trigger group or installing an aftermarket trigger group would be money better spent at this point. It'll put you further ahead. And likely into a better position after some range time to decide if the stock barrel needs to go or not.