Sorry for the delay… 
I was not able to see your web site – I get not found response – to see how do you assign the DOIs and record/register the changes/updates i.e. use the Crossmark.
I read the Crossmark guidelines and here is what I think would be currently possible in OJS and how:
From this page https://www.crossref.org/get-started/crossmark/:
I suppose you have already done the step number 1.
For the step number 2, to create and provide a policy page: either you could use the current i.e. an external page or probably better to create a policy page in OJS using the Static Pages Plugin (and then register that page i.e. update your DOI for the policy page).
The step number 3 also have to be done manually – there is currently no support for Crossmark in OJS. Maybe you could use the regular OJS DOI deposit and then only manually deposit the Crossmark part as stand-alone data.
Step number 4 (Provide DOIs for items being corrected or updated) is the tricky one, I think: OJS supports above all the Crossref DOI assignment on an article level and currently does not track the versions/changes. The Crossmark, on the other side, expects that a new article version has a new DOI in the best case.
Thus, I believe, currently only the “Example3: In-Situ Correction” from this page Crossmark - registering updates – Support Center would be possible. That means that you would have only one DOI for an article and that DOI would not change when article changes. But you would provide different PDFs, e.g. original and corrected ones, that would be linked to from the article view/landing page.
I am not sure if it would also/better work if you would assign DOIs also to the OJS galleys – I would have to think about this possibility…
That’s why I wanted to see how you proceed currently – how do you assign DOIs, on which objects (article or file level) and according to that how do you currently use the Crossmark. Could you explain and show it to me?
Step number 5: if you use the Dublin Core Indexing Plugin there is already this meta tag on the article view/landing page: <meta name="DC.Identifier.DOI" content="10.9876/tj1.v1i2.3"/>. I hope this is enough and would word with Crossmark button, but maybe to double check it with Crossref.
Step number 6 and 7, applying the Crossmark button: according to the “Example 3: In-Situ Correction” here Crossmark - registering updates – Support Center, the Crossmark button should be applied to the article view/landing page as well as PDF i.e. full text files. I am not sure if every article and file should contain the Crossmark button, also if there are not changes/updates? – I believe so. To apply/insert the button in the article view/landing page you would need to insert that piece of code in the appropriate OJS template (that would lead for the Crossmark to be inserted into every article view/landing page) – either to hard-code it or to implemen a plugin or a theme. This should not be a problem.
To apply the button to the PDF files you would need to do that manually when you create the PDF to be published, I suppose using that open source tool “pdfmark”. How do you do it now?
Does this help a little bit?
Best,
Bozana