Does anyone have a good suggestion on how to force DNN to automatically place new pages at the top of the "child tabs" list, i.e. give the new tab the lowest tab order and bump down all existing tabs?

From what I can see, I would have to modify code within the Library to do this, which isn't desirable considering future upgrades.

(DNN 4.4.1 at the moment - considering upgrading)

Thanks, but not what I was asking for ("how to force DNN to automatically place new pages at the top of the "child tabs" list").

With a lot of pages on the same level, moving each new page up using the administrator panel is a hassle. Hence, I'm looking for a way to alter the default behaviour so new pages automatically get the lowest tab order.

Until you upgrade to 5.x, you might consider deploying a temporary modification to the AddTab SP of your installation.  This alteration would calculate and update the TabOrder for the new page accordingly.  

Normally I would strongly advise against such a change in the data tier, but so long as you expect the change to not be carried forward (and the change more-or-less exists in 5.x already), this seems a reasonable middle-ground.  Make sure you fully understand the risks before proceeding along this line, however.

Brandon