This is a problem that is also near and dear to me, and I think the original poster has part of this correct. However, let me add something to the mix. Using duty officers and missions to craft is awesome, but there would still be some loose ends to tie up to make it ultimately cool. Firstly, there is a disconnect between energy credits and dilithium. I would say (and someone can correct me if I'm wrong but I'm level 36 and this is the case for me), that energy credits are not used as much as dilithium. So if we are selling things for energy credits, there are not many things in game to use energy credits to buy with. Hence, we have one important form of currency, and one that is non important.
How about making some crafting or other types of missions cost energy credits? Some kind of prerequisite for having duty missions happen. Right now, with dilithium, energy credits are only useful in transwarping and some new person's things.
There is a second problem that is even more important than that however, and that is how to make crafting more fun and engaging. I believe a good way to do this might be to tie item improvements into a crafting system. Say you find or earn an awesome Fleet type photon torpedo. You could then use your duty officers to upgrade them in a system where for some more work, (And maybe a chance to fail and losing the item which would keep things interesting,) you could use them to make enhancements.
A critical success could even maybe change the item into something better in such a system, say turn a common item to green. This would also give our science and engineer doffs things to do.