Since the barrel will be factory take offs, check to see if they are micro grooved (1/38), or ballard rifled (1/20).
Hence marlin did not produce any of the 444 barrels with deep grooves from lands like you would find on as a win 94 barrel, but isntead went with the shallower ballard and micro grooving rifled barrels isntead. Both of these types of barrels will shoot a .429" jacket bullet at speeds just fine, but if you are loading cast bullets, they have to be sized to .432"~.433" to get a good bite on the shallow rifling/grooving instead.
So really, unless your barrel bore is just pitted to hell and why you are replacing it, it just has shallow grooves in the norm and one of the above replacement barrels is going to be the same as what you currently have.
Bring me up to speed on why you are replacing the barrel in the first place, and if it just because you can't find a bullet that will print, can send you a hand full of my 270gr PC coated .432" bullet to try in the rig.
Note here, if you are still having problem even with the correct size bullet not printing out of the barrel, pull the hand gaurds, the mag tube, and do some single loading bench shooting with the barrel on the sand bags as close you can to the receiver. As noted, if the front hand gaurd/mag tube/mag tube cap are not installed correctly so they causing a funky tension on the barrel, the rifle is going to shoot like crap instead. I have seen a marlin just spray rounds in 6" groups, until the parts where re-installed correctly, and to bring the rig back to shooting 1" groups isntead. Hence the 444 does not use a barrel band, but instead just the tension point of the front mag tube end piece bolt to the bottom of the barrel, and the dove tail hanger in the barrel bottom dove tail for the forearm end cap to thread into isntead. So on regards to the mag tube front bolt to bottom of barrel, easy to set this tension correctly, and again, since the front hand guard clip is the second tension point, a little RVT between the barrel and top of forearm, and making sure that the through bracket is tweak correctly so the hand gaurd is riding even with the barrel, solves a lot of tension problems to begin with.
As for re-barreling the rig if the bore is just pitted to hell (again, both the ballard and micro goove riflinig is shallow to begin with, so don't confuse that with thinking that someone cleaned/worn the rifling out the barrel that way), it's pretty forward since the barrel will be a tension fit. Hence you can use the front receiver scope mount channel for an TDC index mark, one of the two barrel front sight channels as you other index mark, and tighten the barrel to the receive until both at on the same TDC index location.
Worse case, the barrel will not time correctly with barrel tension to the receiver, you will have to set the barrel shoulder back, the back face of the barrel back, then double check the chamber to make sure it still within spec. The tension slot for the mag tube bolt is elongated in the barrel front to back so you will not have any problems there, and the cross dovetail bracket for the front hand guard bolts can be tweaked both sides forward so the front hand guard clip will not having problems bolting back on as well.
To be blunt, short off someone not caring for the rifle to prevent pitting/frosting in the bores rifling to begin with, don't see someone actually shooting/cleaning the rifle enough to wear the rifling out instead. Hence even my 94 44 mag with full loads is a shoulder thumper special that I don't shoot a lot off those loads to begin with, and since it sees mostly mid load with PC cast bullet for fun to be had by all shooting instead, it will be decades of shooting before the barrel even become close before I call the rifling worn out.
If you have doubt on the rifling and if it still good, take a few photo's and post them.
Hell I has seen 25-20's, 32-20's, 38-55's that had barrel bores so bad that you would think that they would not shoot from the effect of black powder loads, only to be pushed to 1k to find the target all day long.