Stripping away the goofy jargon, you want to override the method $obj->does(), i.e. you want to replace the function that gets called. Doing so is no different than replacing any other function:
*{ref($obj).'::does'} = sub {
# do stuff you want
}
This was my original plan but I couldn't seem to get it to work right. That of course was caused by me shooting myself in the foot elsewhere :) Once I resolved the real issue, the problem went away and it passed as expected.
As always, thank you kind folks for your assistance!