I tried to install WWW::Mechanize::Sleepy. I went through all the steps that you went through. I got the same results. The tests failed every time. However, I tried something a little different. WWW::Mechanize-1.18 should work, theoretically, but it doesn't, so I compared 1.18 with 0.58---there are some radical differences between the two. I reinstalled WWW::Mechanize-0.58. After that, I reinstalled WWW::Mechanize::Sleepy, and all tests were successful! The installation was successful.
As far as WWW::Mechanize::Sleepy's not finding WWW::Mechanize, that's a problem with the module---it's not your system. So, give this procedure a try. See: