Ha! No thanks to the Illustrator forum (which didn't give me a single response to my query), I fiiiiiiiiinally managed to find out how to get the transparency saved in my SVG file, via this link...
http://graphicdesign.stackexchange.c...age-trace-help
I saved my SVG file, added it to my "test book", sent it over to the iPad and then changed my background to black ("night") mode, and indeed it comes out transparent (and looks great).
))
However, I still can't seem to get the file size down, and there's still the issue regarding compatibility in some devices -- maybe I can find somewhere that'll help explain how to resolve the former issue, but I guess there's not much I can do about the latter...
...and so I guess I'm still thinking that PNG is probably the way to go (at least for now). :/ But I'm so happy to have figured out the transparency issue, at least!