Most of my dilithium from recent STFs has been getting traded in for Zen for random account and character upgrades (EC cap increase, more DOff slots, etc). I traded in all the blue tech and salvage and most of the EDCs, as well as all the purple tech except 1 each of the shield and deflector (which I'll use on the 2 respective parts of the Omega space set), and I kept all of the purple salvage, which I'll use for differing weapon loadouts.
I'm also in the habit of using my spare ships as an extra equipment bank. What I'm hoping to do is collect a good selection of end-game level ships that give a varied play style, so I can switch for variety now and then. Just not sure which ship I'll get next.