It would be great if we could use "Display on all pages," but unfortunately matters are a tad more complicated. I simplified the problem for the sake of presenting it clearly, but in actuality each page on our site will belong to one of many sections. So things are made difficult by the fact that we may want the same type of module (i.e., FAQ) on all pages, but all pages in one section would contain the same module instance, all pages in another section would contain a different instance, etc.
The Shadow Content module seems to me to behave much in the same way as simply copying a particular module instance from one page to another, just without the ability to edit it from any page. At any rate, it doesn't seem to solve the problem of needing to add a module to many existing pages at once.
As for the last suggestion, I will have to examine it more closely. But am I understanding correctly that this would just be using down-and-dirty SQL to directly update the database records, rather than use the DNN interface? I'd consider this as an option, but isn't it somewhat ill-advised to directly alter the SQL data this way? I'd appreciate a few opinions on whether this is a common way to implement changes in your DNN sites.
Now that I've brought up the concept of multiple "sections," each with their own common content, surely I'm right in thinking it would be a pipe dream to add one module type, but different module instances for each section, to all pages of the site with one broad stroke? For example, if I want to add a FAQ module to the right pane of all pages, but one shared instance for the Products section, one shared instance for the Forums section, etc . . . I'm assuming I'm stuck with, at the very least, manually adding the module to at least one page in each section? (I suppose, if I am in fact cracking open the datasource itself, I might be able to affect a stored procedure . . .)
The main point is: for all this I'm looking at working outside the bounds of the DNN admin interface?