"I ask this question with a bit of caution, as I get the impression from reading through these boards that people who use UAE-type setups generally get treated like "warez kiddies" and are thus looked down upon."
No need to be cautious. As long as someone is running AOS and buying his software (games is an exception, some of the games are in reality not possible to get hold of originally.) I'd say that WinUAE is a perfectly good way of experiencing and using the Amiga enviroment.
Anyway, have you tried copying the whole AOS3.5 cd to your harddrive, read/write enabled all files, and then tried installing again? If this does not work, then I'd suggest you buy AOS3.9 because I can help you with that _guaranteed_ (I've installed it on various computers and it runs perfectly after a few very minor tweaks.). Also I believe that OS 3.9 contains a few more updates...not sure though, went from 3.1 to 3.9 myself.
oh, and I forgot to add that you also could look on cloanto's website for some small tips on installing OS3.5-3.9 in the Amiga Forever.