re: But in the top level “Manage” view it does not work with “Simple Page Ordering” or presumably similar drag and drop plugins (which offers drag & drop ordering of pages or posts or other list view mode)
Right, this is because Connections does not use a WordPress Custom Post Type (CPT) because the database schema is not optimized for directory content. CPT’s are optimized for post/page content.
Providing drop and drag really is only feasible with a small directory. It really does not work well when dealing with hundreds and thousand of entries split across many pages.
re: The fact that there is also no “Quick Edit” mode in list view
Adding this has been long on my list of to do. The manage page is very old code and long overdue for a complete revamp. Honestly, not sure when I’ll get to it but when I do adding a quick edit like feature will be part of the revamp.
re: I found myself still hand writing who’s in what order only to hand-enter each number. With a Quick edit mode, you could at lease visually see all of the entries in their current order.
The entries should still be shown/listed in the order that was set on the manage page so you should be able to visually so who is in what order even though you can not see the actual order number assigned to the entry.
When the manag page revamp is done, it’ll be possible to add columns, perhaps adding a column to display the order number will be helpful. I’ve added that to my feature request list.