Set variables on imported comp?
A normal 'pick-whipped' expression:

thisComp.layer("Solid 1").transform.position


An expression referencing another composition within your project:

comp("Second Comp Name").layer("Solid 1").transform.position


As long as the composition name in Project A is consistent, you could just reference it and include a fallback in case it hasn't been imported like this:

try { comp("PROJECT A COMP NAME").layer("YOUR LAYER NAME").text.sourceText; }
catch(err) { text.sourceText }


Reference:
 https://gist.github.com/animoplex/b426933ae6c896c79ea98a50855ff62e

I figured I'd give this a quick response since it's been a while and there haven't been any answers. Send me a comment if you have questions.

Hope this helps :)