Solid rivet options
It's not easy, but it is possible to do these with solid rivets.
I cut the flanges on the reinforcement angles back at 45 deg, since those bits of the flange aren't doing anything useful from a structural point of view ("adding lightness").
I was then able to just get the toe of a small bucking bar in between the angle's flange and the rivet shank. Took me a few tries, including drill-outs, but it did work ok.
If you don't want to use solid rivets, an alternative to the MK319BS is a Cherrymax CR-3214. These are a blind fastener equivalent to the NAS1097 "oops" rivets.