Actually, we've been able to determine that this isn't a bug but more of an issue with design. The "Series Post Navigation" template in the series options page is more for the general setup of the series navigation attached to posts and does not have the post_id exposed to it when replacing tokens.
You can still do what you want. To add in series part information, there are two field below the template. One for "Custom Next Post Text" (which is used to replace the %next_post% token, and "Custom Previous Post Text" (which is used to replace the %previous_post% token. You can use the
%series_part% token in those fields and it will get replaced as expected.
I hope that helps!