What courses should I apply to for creative engineering / product design?

You have to be careful when selecting Product Design if you want the Engineering side. BA Product Design isn't Engineering. The Engineering course of Product Design is named BSc Engineering Product Design. Some universities like Middlesex sometimes mix the modules with the Product Design and Engineering Product Design to make use of the teachings. You wouldn't be given a Physics module in a Product Design course, you'll find that on an Engineering Product Design course.

Yeah, it would be better to look for a BSc over a BA in terms of applying Engineering or some form of science applyed into it. You will lose the Engineering aspect if you apply for a BA course. Everyone has a way of applying their creative ideas, you'll still get that but just must smaller then an BA. BA goes all out but lose that engineering aspect.

Product Design replaces the Engineering model with a module like Human Factors, having to take care of how we pick up and interact with an object as we use it while it looks good, whereas Engineering Product Design would have a module like building a machine which is safe in the field for everything as well as everyone, from my knowledge.

Yeah, it would be better to look for a BSc over a BA in terms of applying Engineering or some form of science applyed into it. You will lose the Engineering aspect if you apply for a BA course. Everyone has a way of applying their creative ideas, you'll still get that but just must smaller then an BA. BA goes all out but lose that engineering aspect.

Product Design replaces the Engineering model with a module like Human Factors, having to take care of how we pick up and interact with an object as we use it while it looks good, whereas Engineering Product Design would have a module like building a machine which is safe in the field for everything as well as everyone, from my knowledge.