To the best of my knowledge you can't buy an adapter to run the big mount stihl (also the same as a big mout domar with different oil hole location) on a normal small mount Stihl.
It would not be hard to make one if you have access to a mill.
Changing over from 3/8 to .404 is just a matter of swapping the rim sprocket out. If your clutch drum does not have a removeable rim sprocket, then you will need a new clutch drum. Just make sure to get a clutch drum with a removable rim instead of the sprocket as part of the clutch drum. Rim sprockets are cheap, Clutch drums are not.
Also, that long bar is alot of bar for a stock 044. you might have oiling problems as well. 404 is a lot larger tooth and will take a bigger bite out of the wood which takes more HP to run it. i personally would not run 404 on a 440/044.
The other thing you could do, is buy the bar, then buy a 3/8 replacement tip. Then you will have to run 3/8 .063 gauge chain, but you would not have to change your clutchdrum/rim setup either.