Just a final followup, I've tested this thoroughly and it works great.
1. Create a project called global.
2. Create a CSS in the global project named assets/css/company_name.css.
3. Add and push global to the git repository (or however you share your projects amongst your writers).
4. Writers pull global from the git repo.
5. Writers create a directory in their project called assets/global:
a. Right-click assets and select New > Folder.
b. Name the folder global.
6. Writers create linked version of company_name.css.
a. Right-click the new global directory and select Link > Link Folder.
b. Browse to and select global/contents/assets/css.
7. Link all files in the project to global/css/company_name.css:
a. Run a script that updates the CSS link in all files in the project.*
b. Set the default CSS for future files:
i Open File > Project Settings.
ii. Change Default Stylesheet to contents/assets/global/css/altowav.css.
8. Profit.
* I'm doing the updating myself. It's pretty simple, the main task is to add
<link rel="stylesheet" type="text/css" href="assets/global/css/company_name.css" /> to the <head> section of each file. I'm also removing all other CSS from the <head> section, just to make sure that every file is actually using the same CSS. This could cause some problems, if writers are using a custom CSS that has formats that don't exist in company_name.css. This isn't a big problem our projects already use the same CSS, it just isn't managed globally. But if someone else is doing this, you do need to keep in mind that sufficiently complex implementations might be broken by this step.
Note 1: I've decided to abandon the whole "read-only" aspect of this, since it caused weird problems with synching linked files (you have to change the permissions to get it to work correctly, and RoboHelp's messages weren't helpful and sometimes reported that the sync failed even though it didn't). So now, writers will be able to change their local version of company_name.css, but then if they synch to the global version, they'll lose their local changes. I'm not terribly happy with this outcome but it's still pretty good, all things considered. Most writers aren't going to go changing the stylesheet. They'd much rather have me deal with it.
Note 2: This same process can be used for other files that you want to be global and static. I haven't started testing this, but I ought to be able to also do this with the cover page, so that we can centrally manage all of our cover pages, which will be pretty slick.
Your team need to watch for that and seek your instructions as to whether or not to repeat the process of creating another copy and moving that to the CSS folder, deleting the old file and renaming the new one.
If you look at my step 7, above, you'll see that this isn't how I'm implimenting it. I'm using the linked file for the CSS, rather than copying it into assets/css. Interestingly, RoboHelp doesn't seem to care where the CSS is stored, so long as it is stored within the project somewhere. So it can be assets/css, or assets/foo/css, or whatever you'd like.