Gotcha, sorry for the misunderstanding.
There is still a reason that blanket scaling only works in some situations. To do what you want, you have to modify your families to be parametric in order to change their size. I know you said you don't WANT to do that, but there is good reason it works this way.
Revit is designed to be a digital representation of a real world or soon-to-be real world building. Real world things don't just scale the way you are talking about. Back to the my initial table example, when you make a table bigger, the whole thing doesn't grow at an even rate. If I scale it to 1.25 its size to fit more people, then it also gets 1.25 times taller, and all of the individual components, like the legs, get 1.25 times wider and thicker. That's not typically how you'd make a bigger table.
This is why most families are parametric, where individual components are driven by parameters that you input. There are ways to link those parameters together, so you could have a custom "Scale" parameter that drives everything else. I'm not sure how complicated your clients logos are, but it should be possible to do this. Not saying it'll be easy, but if your putting these all of your model, it'd probably be worth the time.
The other option is to not create such detailed signage everywhere. The only time we place modeled signage is if it'll show up in a rendering. Everything else is just a plain rectangular prism that has text annotations for scheduling, but that text isn't actually modeled.
Its up to you how you want to handle that. But I don't there would be much support for incorporating this feature as you're asking for it, as it breaks one of the core functions of Revit.