Results of a quick perusal of MMPDS-04 for densities of steels:
All of the low carbon steels such as 4130. 4340, 8630, and so on: 0.283 pounds per cubic inch (pci)
Custom 450, 455, and 465: 0.28 pci
PH13-8Mo: 0.279 pci
15-5PH: 0.283 pci
17-4PH: 0.282 to 0.284 pci depending on the heat treat condition. (Seems odd, but there it is, in black and white.)
17-7PH: 0.279 pci
The austenitic "18-8" or "300 series" steels: 0.286 pci
The 250 and 280 18Ni maraging steels: 0.286 pci
When I get some time I'll pull up an AMS for 416 steel alloy to see where it falls, and whether the density is given to two or three decimal places; I'm curious. In any case, 0.29 pci is probably a safe number to use if the external dimensions of the finished barrel are held reasonably close. The diameter squared effect on cross section area adds weight quickly if the barrel is left a little fat. The cross section area of a 1 inch nominal OD barrel left 0.010 inches over increases by a little over 2% (1.01^2 ), which is about the same as the difference between using 0.28 or 0.286 pci in a calculation of weight.