I upgraded using the recommended path (05.04.04 -> 05.05.00 -> 05.06.07 -> 06.01.03 -> 07.00.06).

If as host or admin I click "Edit Page" | "Edit This Page" the black Edit, Settings, and Move icons appear and function as they should.

For a user in a role that has only edit permissions on an individual HTML module, the black edit button does nothing (and is not placed in the correct position). From reading forum posts, it appears that the needed libraries are loaded by the top toolbar, which the user with only module edit permissions doesn't have, so this is why it's broken. How can I fix this?

Chrome console shows:

Uncaught TypeError: Object [object Object] has no method 'dnnConfirm' ModuleActions.js:162
buildMenu ModuleActions.js:162
$.fn.dnnModuleActions ModuleActions.js:45
setUpActions mypage.aspx:98
(anonymous function) mypage.aspx:169
f.event.dispatch jquery.min.js:3
h.handle.i jquery.min.js:3

Things checked and tried:
jQuery is not being loaded in the skin ascx file (reference: Skin causing JQuery conflicts? )
Enable Skin Widgets is checked under Admin, no extra language packs are installed, and web.config contains references to ClientDependency and ClientDependencyHandler (reference: Javascript errors: draggable and dnnConfirm not a function)

I tried this workaround as mentioned in the last thread: 
Added to my skin ascx file:

DotNetNuke.Framework.jQuery.RequestRegistration();
DotNetNuke.Framework.jQuery.RequestUIRegistration();
DotNetNuke.Framework.jQuery.RequestDnnPluginsRegistration();

Although this made the buttons function correctly, it completely changed the skin - adding extra styling, a menu bar that I didn't want, copyright notices for DNN corp at the bottom, etc.