MG 08/15 - range 2000 meters effective, 3500 meters maximum. 8mm. At 40 pounds, it would need to shed a little weight to get town to the M240B’s roughly 28 pounds. Swapping out the wood for lightweight composite would be a good start. Or modifying it to air cooling would easily meet the weight (see the 08/19.
So it sounds what they are looking for was readily available 100 years ago.
Any cartridge of that power such as .308 would easily go that far. Almost all military rifles of those days had volley sights or similar out to 2000 meters, or more.