So, the classic code as shown in the Camel Book simply can't work. If you don't use Try::Tiny (or compatible system? Do they interoperate properly?), you can only use $@ once.

Once? Try not at all. See the other messages in this thread. Pre-5.14, $@ is unreliable (and post 5.14, your problem won't magically solve itself - and I doubt Try::Tiny can determine why a block died without looking at $@). Never use $@ to determine whether an eval succeeded or not. Just use its return value. I'm not saying one shouldn't use Try::Tiny, but I do want to point out that safely determining whether an eval succeeded or not does not require a module:

eval {
    ... your code goes here ...
    1;
}
or do {
    my $err = $@ || "Unknown error";
    ... error handling ...
};
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