This is kind a summary of what was said, feel free to take any bits and post your ideas or if you have some other idea for a different aspect of the game.
Crafting as it stands is very weak, “take item X to person A, person A then allows you to modify item X in a few ways.”
This is not a true crafting system and seeing that item creation is a part of the Star trek story this is inadequate for the game. Take for example Star Trek Voyager: Scorpion the first time we meet the undine or species 8472. The crew is forced to not only assemble a cure for a crew member but also has to weaponize the cure and create the weapons to deliver the weaponized cure. Here we see 3 forms of crafting.
2: weapon enhancement
3: weapon systems
The crew is also able to salvage from what remains of the Borg equipment and they make enhancements to many other systems in the ship. Reviewing the episodes around this one shows a continuation of those improvements. In every star trek show the crews of the various ships have had to make new items and technology or make improvements to existing ones. The self replicating mines from late in the Deep Space Nine story. The enterprise in Next Gen reconfiguring the deflector to emit a high frequency pulse to protect against the crystalline entity. The list goes on.
Now that we have established the need to make crafting real system and not just a vendor I will discuss a possibility of what such a system could look like.
First the players could make anything from a hypo spry to a phaser beam array using materials that they already collect on missions and during exploration missions. They can make say a phaser then before “finalizing” the item could opt to add a spec ability to the item, I.E. crit chance. Again using some of the materials they are already available in game.
When the players begin gaining more skill points in crafting they could then begin to specialize and it could be as simple as Choosing from weapons, consoles, or shields/deflectors. Alternatively It could also be something as complex as going from basic weapons, to energy weapons, to phasers weapons to phaser beam arrays and so forth.
Also as expanding the ship is part of the current goals for the dev team you could make a special room on a player’s ship that you only get from crafting and as your skill goes up that room could get more and more advanced both in appearance and function. I.E. the Astrometrics lab in Voyager.
Implementing such a system could be done while still using memory alpha as the starting point and mayby for where the trainers would be. So you could use mostly existing assets while still implementing a part of the game that is both vital and fun.