What version of Perl are you using? I get the same results as you on an old box with 5.8.4 installed, but on my main box with 5.10.0, I get different results: $INC{module.pm} is undef if require module dies, and calling require module a second time fails.
In both versions, I can trick the require into trying again, and producing the original error message for me, simply by wrapping my own call in a little localisation:
{
local %INC = %INC;
delete $INC{$sFile};
$result = eval "require Monk::Foo::Bar";
$error = $@;
}
Though, on reflection, that has obvious issues for modules that really don't want to be loaded more than once, so maybe it's not a good idea.
