> While I think that converting "0.0.3" to "0.000003"
> isn't the correct way

It's the official way. Please read perldoc version.

> it thinks that "0.2" is a newer version than "0.11",
> because it considers "0.2" to be a short hand for "0.002"
> and "0.11"

Wrong. It considers 0.2 > 0.11 because perl does:

% perl -le 'print 0.2 > 0.11 ? "T" : "F"'
T

> most people will consider "0.01" to be a newer release
> than "0.0.3".

Thank you! I couldn't agree more!

> I would consider "0.01" and "0.1.0" to be equivalent

Sorry, the factor 1000 has been chosen to be the perl mapping for each dot in the version string.

> I suggest you keep 0.01 in your CPAN dir, and name your
> new release "0.1.3", or "0.2.3"

Sorry, it would have to be at least a little bit more than 0.10.0, because 0.10.0 is the equivalent of 0.010000 and as such is exactly numerically equal to 0.01.