So how do you go about installing them without screws?
My responses
1. Butyl tape --
2. Use the same thickness acrylic that you have currently.
3. I believe your Grampian has framed windows with trim pieces that cover.the window edges -- you don't have a frameless system. Install it the way it went in in the first place. (It's been in there for over two generations...)
4. Be very careful drilling any holes in acrylic -- or you'll get cracking. You have to use a special bit , over drill the holes, etc. Do the screws go through the acrylic now -- or are the holes outside the windows?
5. If the trim pieces have sealant on them (in addition to the butyl tape) then use a LITTLE sealant. (NOT permanent 5200 -- something that can be released later, if needs to be.)