How do you package your DLLs for TestComplete to consume?

Automation projects don't "compile" anything into any packages.  There are no DLL's or anything like that that would be applied or imported or anything.  So, putting the code units into a separate project won't help you.  For an automation project to utilize a script unit, that script unit needs to be added to the project (Right click on script node in project explorer -> Select Add -> Select Existing item -> Browse to code unit and click OK  See https://support.smartbear.com/testcomplete/docs/scripting/calling-routines/declared-in-another-project.html).

The alternative would be to turn those common code libraries into Script Extensions of runtime objects.  See https://support.smartbear.com/testcomplete/docs/working-with/extending/script/index.html.