I know I can sell a project and own the copyright (as long as it's not shared), but can I sell a remix, remove all copyrighted material from the original project, and add my copyright property as long as I give the original project credit? Do I have to worry about anything?

This is the license scratch uses, I'd suggest you read through that. (That's the readable version- if you really want to make sure, this is the official legal version.)
From that, I'd say yes, you can- under the condition that your project is also licensed under the same license.

Yes you can

This question is essentially answered, so I'm gonna close it. Thanks for your help!