All classes are in the same monolithic source file. USE doesn't appear to like that and searches for actual .pm files...

That is correct. Since packages almost always have a one-to-one relationship with .pm files which share the same name, it's easy to start thinking of them as interchangable, but they're not.

use specifies a file to read, no more and no less. The package(s) contained within that file are defined solely by the package statement(s) it contains.

For example, if you have a file named Foo.pm containing

package Bar;

use strict;
use warnings;

sub hi {
  print "Hello, world!\n";
}

1;
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then you would load its contents with use Foo, but execute them with Bar::hi. This is, obviously, a little confusing in most cases, which is why the convention of using the same name for the file and the package exists. But it's just a convention, not something enforced (or even recognized) by the language.