Actually, I don't think that matters at all.
SotM is all about dividing your resources. You need to kill the villain to win, but they stop you by throwing out distractions. You need to destroy Omnitron, but you will need to divert your resources and deal with the Electro Pulse Explosive. There are many different ways that the villain "distracts" you. For example, adding on DR, making you lose cards, hurting you etc. This is often done with different minions, Ongoings, etc. I am not going to go into all of the ways now, but for simplicity, when you attack the villain directly, you are trying to win the game, while attacking anything else is preventing you from losing the game. Often this is done by giving you more rounds to hurt the villain. If you know you can kill the villain before you lose, then there is no reason to deal with the distractions.
This is one of the reasons why Tempest is very powerful. With Squall and Gene-Bound Shackles, he can use his Play and Power phase to deal with distractions, while still hitting the villain. Tempest doesn't really need to divide his resources.
This is also one of the reason why Baron Blade is so easy. His additional lose condition forces you to attack him directly and avoid the distractions. Essentially, by hitting him you are fulfilling both "win the game" and "don't lose the game." This prioritizes your resources, and you often you can kill him before you lose.
Now let's take a look at Gloomweaver. As soon as a relic hits the table, were is your priory? Let's look at what happens if you attack the relic:
1) All the relics have a nasty effect, and removing that effect can help you not lose. This alone won't prioritize the target, but it just acts like any other cards.
2) Destroying the relic prevents Gloomweaver from flipping. Since his flip side is harder than his setup, by destroying the relic, you are giving yourself even more chances not to lose.
3) Gloomweaver's flip side heals him. So, there is very little to prioritize Gloomweaver over the relic. If you focus on him, and the third relic hits the board, you just undid everything you were trying to do.
4) In addition to all of those things that will help you not lose, you have an explicit win condition.
5) The explicit win condition has a total hp less than Gloomweaver himself.
There are many reasons to take out the relic first that it should be your main priority, and there are very little reason to divide out your resources. Now, there is a way for them to come back, so in addition to taking them out, you also need to kill cultists so that the relic is buried in the trash. This puts hitting Gloomweaver himself at a very low priority (and his advance mode can take that away completely).
The only time it is worth to hit Gloomweaver himself is when there are no higher priority targets. If there are no higher priority targets, then by all means hit him. Now, it is true that you might now get all of the relics and win that way, but it doesn't change the fact that this is the best strategy against him in most situations, and the relics are the first thing going down.
In order to "fix" Gloomweaver, I think it is worth finding out why he is so easy.