Do LED lights work well for CAT III B operations?
I don't know if you can do Cat IIIB with a HUD (I'd have said that you're limited to Cat IIIA with one, but somebody may have a capability I'm not aware of) but no, LED lights generally don't wash out a HUD any worse than other lights do.  If your HUD brightness is sufficiently dim, then bright enough lights of any sort can wash it out, but that just requires you to turn the brightness up a bit.

I've never heard of or seen any "Sea of Blue" effect from LED lights, and I don't think LED lights have particularly worse glare (or any other) characteristics when used as runway lighting.  They're somewhat distinctive, but not particularly worse.

If LED lights have regulatory approval for what you want to do, I'd say that right there is the answer to your questions.  And if they don't, well, then that's also an answer.