Undaunted Unweaver + Undaunted Infiltrator; Do They Stack?

Wondering if the Undaunted Unweaver and Undaunted Infiltrator 5-piece set bonuses will stack with each other?

I have a Sorcerer friend who insists on doing a hybrid DPS build, so I'm trying to work out a set combination that will emphasize this. Thinking of the above 2 sets and taking advantage of weapon swapping to get both 5 piece bonuses; Unweaver will be active when he has 2H out, and Infiltrator when Staff is out. However, will the bonus be lost upon switching weapons, or would he be able to switch Staff, cast magic stuff, go back to mainbar 2H for Stam stuff, and maintain both bonuses, if they even stack at all?

Are there any other sets that might work with this? Some others stand out, like the one that equalizes Spell/Weapon damage based on the higher value combined with something that rises Weapon damage, but he doesn't have Morrowind so it's out of our reach right now.

inb4 hybrid builds aren't meta; I know, I've explained this, and he cannot be convinced to change. Regardless, the build will be used primarily for open-world play & Normal dungeons, at least until he has fully upgraded gear & Weaving down well enough to pull respectable DPS. So putting the obvious aside, what are some decent gear options to pull off a hybrid build?