I think it is time to provide an update.

I got two Halo II sweatbands as well as Gutr band, along with riding glasses.
I have been switching between the bands now for a few days, and at times both Halo II and Gutr have eventually failed in stopping the sweat from getting into the eyes. I guess it is just a combination of 90 degrees weather plus me sweating like a pig. Between Halo and Gutr, I do prefer the Gutr though, mainly because it is easy to reuse it, whereas Halo II bands need frequent washes and also need to be a pair.

I read in one of the randonneuring blogs that "two is one, one is none". I think it applies to commuting too.