Simple solution, load a new instance. I speak from experience with UT, TH, and Diplo at 400. Do I ever have a problem? No.
This is what I do. I look and run the missions I want and then atleast 2 of what I don't want. Then I immediately load an instance (leave or enter the ship for example) and look at the missions again. If none available, I load a new instance. So far the most I've had to reload in a row was 10. 10 seems like a lot but consider that an Abundant+ mission for mats is around an hour, 10 reloads is nothing. Anyway, when I do get missions I want, I drop the bad missions my companions are doing for those. Dropping missions means you simply get the mission cost back, so you don't actually lose anything.
The reason I run bad missions in the first place is to take them off the list of possible missions. You can't have a companion run a mission that another companion is currently running, so taking as many bad missions off the list means a greater chance that a good mission will pop up.
Is it annoying that I have to trick the game like this? Yes and no. Yes because I of course want what I want right now when I want it, but no because I understand why the crafting system is set up that way and somewhat agree with it.
If you want to do this, it's good to know how many Mod, Abund, Bount, and Rich yield missions there are of a specific reward. For example, in both Bioanalysis and Archaeology, there is only 1 abundant compound and 1 abundant power crystal mission at grade 6. So reloading for more is stupid.
As I see it, there are two problems with what you have stated.
The first is that the current system does not stop people from getting the available missions they want, it simply makes doing so frustrating and annoying. Making things frustrating and annoying simply turns players off and is not good game design.
Better design would be to allow players to directly select any possible available mission in a given tier, and balance the supply through the number of concurrent missions available and the mission returns.
The second goes back to balancing mat supply with mat demand. Even if we assume the probability of any given mission appearing in the list is the same as any other mission, we still are left with the fact that metal has a significantly higher demand than cloth, yet does not have a higher number of possible missions.
Solutions here include increasing the number of metals missions so the ratio of metals to cloth matches the demand / usefulness to simply removing cloth and having all crew skills use metals to chainging all force crafted items to use cloth and all non-force crafted items to use metal.