Are the hooks in the dashboard such as “load-$page_slug$” and “admin-head-$page_slug$” reliable and consistent throughout installs?

I’m not exactly sure, if I get your question correctly, but…

Yes, these hooks are native WP hooks:

So if you create such page on given WP instance (for example you create it with your plugin/theme and that plugin/theme is active on that instance), then these hooks will get fired.

Of course if such page is not added on given WP instance, then that action won’t get fired… (But how could it – if there is no such page, then it can’t be displayed, then no actions will be run while it’s requested).

I hope it answered your question.