That B737 idea isn't so crazy, actually. Lets take two B737 models for comparison. First is b737-300, model that first flew in 1984, so early 80s tech. Second is b737-700, first time flew in 1997, so its mid 90s tech.
Their length is very comparable to h-6, boeing 300 has 29 meter large wingspan while boeing 700 has same wingspan as h-6. Furthermore, boeings have larger, wider bodies, bigger tail section, bigger engines mounted on pylons, etc. Now, of course it's impossible to accurately guess drag but it's safe to say that boeings, while having considerately bigger frontal surface made drag, have less skin friction drag, less induced drag, better shape overall. For the sake of this post, i'll assume drag levels are similar.
To make long story short: B700 has like 102% maximum range of H-6 while carrying 500% bigger payload. Its empty weight is same as H-6 but it achieves the said range carrying just some 66% of the amount of fuel H-6 does for its range. Engines provide 89 kn thrust, quite comparable with h-6's 93 kn, i'd say. If one could use same level tech engines on h-6, that's 15 tonnes of payload delivered 6000 km away. No matter how you look at it, thats at least 2000 km combat range, with nice reserve to fly faster if needed. Just for extra information, B700 normally uses up 2070 kg of fuel per hour at normal flight conditions for such longest range scenario.
But lets say such mid 90s tech engines just isnt available to china. B300 weighs 33 tons, or little under 4 tonnes less than h-6. its max range is 80% of that of h-6, but it carries 14.5 tons of payload to that range. Knowing that it carries 16.3 tons of fuel, one can calculate that it'd need 20.35 tons of fuel for h-6's range. That'd lower its useful payload to just over 10 tons, but that still beats h-6's figure of mere 3 tons. For comparison, b300 engines use 2250 kg of fuel per hour at normal regime for max range.
Even old B737-200, which first flew in 1967 and its engines are mid 60s turbojets and not turbofans has 4900 km range for some 12.3 ton payload and its engines use little over 2800 kg of fuel per hour for that max range.
Conclusion is, of course, same as in the earlier posts (only then i was just talking out a gut feeling and now i made a little bit more precise guestimate) - just by using different engines h-6 can be turned into a great platform, carrying 10 tons (sinodefence says 9 tons is max, perhaps structure cant support more?) to at least 2000 km away, perhaps as far as 2500 km depending on the flight regime. 3 tons could be delivered to over 8200 km distant place (ferry range), or like 3000-3500 km combat range. Pretty impressive figures and definitively enough for a stop-gap measure plane until true indigenous, next gen bomber flies.