duramax overheating

Most of your problem is in the intake. Hot air off the radiator is getting sucked into the filter housing, up to the turbo, which has to work harder to compress the hot air, which makes a hotter air charge going into the intercooler, which ends up pre-heating the air going into the radiator more then normal, which makes the cooling fan run more. The hotter air going into the radiator means there is less of a temp difference between the air and coolant, so the efficiency of the radiator drops, meaning the coolant temps rise. You can get the LBZ parts from the air filter to the turbo elbow and eliminate thate issue - but it will not be CARB approved. You may want to look at an aftermarket cold air intake (I run a banks with scoop). After you have the intake side taken care of, if you still have overheating, look on diesel place for a overheating lly's...

The LLY Duramax has a smaller fan than the previous LB7 or the '06 model LBZ. I don't know if there's much to change there. The other issue is the turbo mouthpiece is a poor design. The largely accepted solution is to install the mouthpiece from an '06 or early '07 with the LBZ engine. You could probably find one at a wrecking yard. Or, just buy the after market replacement.

2004.5 and 2005 LLY seem to have this issue by poor design.

Duramax LLY overheat search results

Same talked about on DieselPlace forum

Sorry I have not read anything on related radiator hoses.
And I think the solution is more complex than just a hose.

Don't believe it has anything to do with the cooling system. 05's were prone to overheat due to "Thermal Feedback" caused by too tight of a turn in the turbo mouthpiece. Easy to replace. Parts available from somewhat controversial "KillerBee Performance" or AFE. I have the Killer Bee intake overhaul kit and although a little more expensive all the parts are there and you just bolt on.
Read up on thermal feedback on the LLY motor before you change any radiator parts.
overheaters

the 05's had an inherent issue with overheating when towing. I have a friend that has been fighting this for years. Another friend who owns a diesel performance shop said it's very common.

This sounds improbable IMHO. I recommend you get 2nd and 3rd opinions. I first became a little more skeptical about claims when a young man in Moron Country California emphatically insisted his TR-3 Triumph would not crank unless there was a steel chain dangling from the bumper making "earth ground" contact. The year was 1966l.

The best opinions come from radiator shops AFTER they have pressure tested your system and cap.