I do not have experience repairing glasses but i do have 20 years of experience building and converting plastic miniatures ! (used to work for Games Workshop)
What I read here is very close to the perfect solution in my opinion.... use a tiny dot of paint or ink on one side of the break, put the two parts against each other so the dot is in the same place on both sides .... drill the holes in the same place ... use a metal pin or some metal wire (can go as small as paperclip size if the frame is thin, and glue it in the holes as you glue the frame back together (make sure the hole is slightly wider than the pin do glue will fit around the pin) ... this gives a much larger surface to glue and even if the plastic breaks, the pin will still hold the plastic together ... if you use a pin that is thicker and stronger than paperclips then it will also provide more strength to the frame in that spot and it ill bend less so it will no longer break in that spot since it's now stronger than the rest of the frame.
This technique used to be applied all the time to metal miniatures because no glue would hold certain parts together because the area to glue was too small and the weight of the part too heavy. (Imagine having to glue a tiny arm on a 2 inch model but the arm is also holding a huge hammer or shield and weighs more than most of my Oakleys do ).
Thanks! That sounds exactly what I had in mind to try, but the devil is in the details, and I am glad to get your input, and to hear that this could work. I have just gotten hold of a pin vice and micro drill set, so that I can drill the holes by hand. I may try to take a thin nail, cut the ends off with my Dremel, and use it as you've described. That will prevent flexing somewhat in the repair zone, as it'll be stiffer than a paperclip or wire.
I know that to some, this may seem like overkill, but I do love a good project.
I'll try to document the repair job, assuming it works as planned.