It may be anecdotal "superstitious nonsense" but what I have found is that if I send companions on all mission types (whether I need them at that moment or not), I tend to get the missions I do want more often.
Furthermore, I have also found that if I do get a string of one type and I do them all, eventually the string ends and for a while I get none of that type. As a matter of fact, there was a point where all I wanted was companion gifts from UT (I was trying to increase companion affection for an alt) and I did nothing but gift missions and then one time I actually got ALL fabrics and metals missions; zero gift missions. Of course I took full advantage of it
The adage, "a watched pot never boils" rings true here. If all you want is metals you are not going to get enough metals missions to satisfy your need. All the tricks of relogging and whatnot only add to the frustration. IMO, you need to do missions that you do not need the results from right away in order to get what you do want. You can then either sell what you do not need so you can buy what you do need, or simply stockpile those materials until you do need them.