Actually, the H-6 (Tu-16) has been in continual development. And while this may not serve our desires, as we'd like to see China advance in this domain as they have in fighter development, I do believe that the H-6K is the ultimate evolution of this platform and will form the basis for the capabilities of the next generation platform. Also, remember that China's defense policy is still guided by considerations of defense. Long-range strategic bombers aren't quite defensive platforms.
That being said, when development of a new platform does progress, I'd expect the targeted range to be more in the area of 5000km. This range would allow complete coverage of two areas of primary interest to Chinese strategists, those being, the Second Island Chain in the Pacific, and the 'String Of Pearls' that runs from the South China Sea through the Gulf of Thailand, Andaman Sea, Bay of Bengal, the Laccadive and Arabian Seas, the Gulf of Aden, to the Red Sea. The reason I suggest this range and not the 2-3000km, suggested by i.e. below, is that I'd expect Chinese planners to assess the probability that some strategic missions would be best accomplished by a payload of LGBs.
I think that China is wisely preparing it's defensive capabilities first. Although their fighters are multi-role platforms, their primary function, presently, is to provide China with an effective active component of their air-defense complex. Let them get the J-10, 11, 15, and 16 programs (with domestic engines) into full production, and the J-20, and 31 programs into the pre-production phase, then let's see what they have in store for regional air-power projection.