The Steamrunner class (at 315, not 350 meters in length) is 29 meters shorter and has fewer decks than the Intrepid class but is 105 meters wider, with nearly the same volume and therefore mass (despite a lot of empty space behind the main hull): 688,000 metric tons to the Intrepid's 700,000.
At the 355-meter length, its volume was about 15,000 cubic meters greater than the Intrepid. Scaled down to 315 meters, the volume of the Steamrunner would be about 450,000 cubic meters. At the same density as Voyager, it would thus be slightly over half a million metric tons (about 515,000). Since Voyager is a lot more dense than Enterprise-D, I would suggest to use a slightly lower density figure for Steamrunner, and go with 500,000 as a max.
Or 474,474, or maybe 447,447 if it has very large internal spaces for shuttles, or something with 47s in it

I do kinda wish the fandom would just get together and call it "Streamrunner." Immortalizing typos bums me out.