Brazier riverts are hard to find in smaller sizes and lengths--they seem to be popular for assembling semi-trailers, so they're big and long. Not what we need. But they can be found if you search. Same goes for the rivet sets.
I wanted 1/8" Brazier and 5/32" Modified Brazier so that the heads would be the same size, even if I had to go oversize with a particular rivet. My big disappointment is that the Modified Brazier heads don't fit the Brazier rivet sets very well.
Here's an example of the difference between the appearances of the Brazier and Universal heads. As you can see in the right photo, the Brazier rivet heads still look the same. I decided I could use universal heads on a patch that was self-contained around its perimeter, but for the patch that went under the door frame, the rivets had to look like the rest of the heads in the door.
I can also confirm that you need to take extra care not to make smilies when using a Brazier rivet set.