I think this should not be fully automated. Rejecting all non-signed mail is too strict, and changing subjects could be annoying too, and this time it will annoy your own users. Also consider the amount of stress for all parties when you finally apply this system, the day when your users suddenly won't be able to receive a lot of mail that was perfectly working yesterday, or when a lot of mail happen to have this garbage in the subject. I bet they will press you to revert the change, rather than trying to convince their peers to press their admins — this will be by far easiest apparent resolution for them.
You need to consider each domain on case by case basis and what can be automated is statistics. On reception you can collect the counts for each sender domain, how many mails it sent to you, and how many of them appear to be human-made and how many reverse traffic is seen (e.g. replies).
Then, you may select the domain which showed substantial traffic and build notices to their postmasters or domain owners in a semi-automated fashion, or, perhaps, apply the processing that is suggested in other answers only to those domains, or convince only a few users who talk with those domains a lot to add notifications in their MUAs. This will make the whole inception of the system less stressful, notices will be addressed more directly, while you won't bother notifying the operators of systems from which you had only seen only a stray messages without any response in their direction.
Update. Technically you can use something like this solution to create your notification emails. But again, I strongly advise you against sending such notifications to end users. They don't bother whether mails are DKIM signed or not. Email RFCs define postmaster@<domain>
address for such notices.
If a part of email traffic from a domain is signed, and part is not, I think it is not worth writing to a postmaster at all. They prove they know what DKIM is because they are using it; the fact they don't use it for some mail could only mean they know what they are doing and there are reasons for doing so. If there is a DMARC policy, you should comply with it, because it is the manifestation of their view on the problem, and your notices and explanations won't do any good at all.