Personally, I'd rather see a storage pane set up like the materials tab for mini's, either for ded or unded that'll hold one version of each. And that if you did dedicate it and sell it then it's gone, you don't get to bring it out unless you acquire another.
And if you really wanted to play with your dedicated mini's then you can activate them ONLY in your HoM.
Dedicated Minipet Re-Acquisition
Jayden_Angelus