In general, you focused the points to adress:
From an engineering point of view, to not allow "dead areas" where tablets or tablet chips can stay from one product to the other.
Of course you will not be able to avoid all these dead areas and that where the procedures, verification and discipline come in. You already know where are these areas, if can be enginnered to close it, do itr, the others you will have to rely on the persons.
It is always usefull to have a packaging responsible that you can draw the attention regarding these points.
In a multiproduct pharama that I worked our packaging machines were also not dedicated. Each of the blister machine+cartoning machine had a person that was the ultimate responsible to have teh line working and specially to assure the cleaningness.
One source of contamination that persons usually forget if the staff itself. During the packaging operation do you have staff that is not directly related with teh operation hanging around?
Finish with it and limit acess to those areas. If you limit the acess then you can have persons responsible for the area that you can train.
Other good thing to do is to give some general training to the staff regarding this problem. If you still have it is because the line staff doesn't take so much attention to it.
Go to the internet (and FDA website) and take examples of Forms 483 that pointed out cross contamination issues. Then use also some examples of labs that had to close or saw their revenue strongly affected because of FDA audits and translate that to your company. Eventually you can also find cases of civil suits or call of products because cross contamination issues.
If you deliver the message that "This issue is against all GMP, FDA, ICH regulation, someday authorities will close our door and everybody goes home.",then they might be attentive to it.
Try to put everything in terms of money (lost business, lay-offs, etc. ) and persons will easily understand.
And if the older ones come with the same old story "We have been doing this for 30 years and up to now there was never a problem" tell them the story of Able Labs.
Sorry for the long post.