Here's a Challenge...
I want to take a group of friends out for a nice breakfast or brunch. One friend is strict vegetarian (no eggs) but does love all kinds of breakfast breads, including waffles and pancakes. Another friend is Muslim and eats halal exclusively. Any suggestions?
Your friend list is far more eclectic than mine, so these are things to which I have not given any thought. If I were taking a group of my friends out for a nice brunch, we'd go to Hugo's. Of course, I haven't lived in Houston that long, so am not aware of all of the options.
So if, given my limited knowledge, I were somehow tasked to to host a group with a wide range of dietary concerns, I'd start with the big hotels. They have to offer something for everyone and it has to be nice. I know that in particular the Four Seasons often has guests from the Middle East here for the oil business. And if I didn't like what I was finding at the hotels, I'd probably look toward some of the Indian/Paki, and vegetarian restaurants to see what they've got.
I don't know of any Halal restaurants open before 11 or 11:30; Kosher, yes, but not Halal.
Suggestion: go to b4, pull up their Halal category, then their Vegetarian category and see if there are any on both lists?
Or go to zabihah.com and pull up the Houston lists and start working your way through it. We have as many Halal venues as the whole rest of the state combined so there's got to be something.