I dont think I am the best person at all to answer this question but I have a small bit of knowledge about some of it. PM Gamerprinter perhaps ?
I do know a lot about drilling plexiglass tho. Plexi-glass normally refers to acrylic (instead of polycarbonate) and acrylic comes in two types which is extruded and cast. Cast is normally clearer and drills just fine tho it can shatter if its stressed a lot. The extruded stuff instantly melts on a drill bit and gums up. Then it cools and solidifies the moment it stops and embeds your drill bit into it and its hard to get out. Extruded is cheaper and normally used for secondary glazing so its 50:50 which one you might have on a picture framing job. If you do drill it then do it slow with a small bit and then let it cool for a minute or so and then use larger bit and work up to your final size. If you go with a wide bit and fast to start with then it will gum up or shatter.
So I say - Dont drill it !
I can tell you this tho. You can buy small bits of acrylic online for not a lot. 3mm is very popular thickness. You can get some of that and cut it out and drill that bit instead. If you know you have bought Cast then you will be fine and if you screw up you can try again. To attach one bit of acrylic to another is simple *IF* you use the right glue and there is only one right glue and its called plastic weld cement - or Dichloromethane.
This:
https://www.amazon.com/Weld-Acrylic-.../dp/B0096TWKCW
or
https://www.amazon.com/EMA-Plastic-C.../dp/B00QQNNWIW
or any similar provider of the same stuff.
Its like water but it evaporates almost instantly so usually you need an applicator bottle. You can use a paint brush and thoroughly wet it up and get it on to the part quick. You put two pieces of acrylic together and only then apply the water thin liquid to it and it cappilaries into the joint. About 20 seconds later its firm about 10 minutes later its as though it were one piece of acrylic. Do not try to apply the glue to one part or the other or the place where its going to fit then put them together after. Put the pieces together first. Try it on some spare and see then you will get it.
Reviews saying its rubbish stuff usually have people applying it wrong because it just evaporates and does nothing. It doesnt glue anything other than acrylic either. Its not like normal glue.
So you can make your own mounting lugs out of acrylic and glue them on.