39 Articles in Modern English

It is selected by your prioritization.

Nor do I ...

I've been reading in the ACNA Catechism.  It has references to individual entries of the 39 Articles.  The references are taken from the book "The Anglican Tradition:  A Handbook of Sources."  It does link to a correct entry, however, it uses the 1571 Articles.  The 1662 Articles with modern English spelling is also included in that same book.  Is there any way to get the links to go to the 1662 39 Articles, or is it hard-coded?

In fact, the references/links should not be hard-coded to a specific book, but should be datatype links to a datatype for the 39 Articles. They will open the highest prioritized resource that contains the datatype (rather than a specific book). Assuming that is so, you can find out which resources you own that contain the datatype - with a power lookup on the reference - and then re-prioritize according to your interest.

Note: I personally don't own the Logos-edition of the Anglican Catechism, I have a PB where I put in the datatype link. It will by default link to and open AT:HS, as your copy does. Now when I right-click on a link - here the link to Article 6 in question 27 -.and have the context menu show the Reference, i.e. the 39 Articles (which is where in bibles usually a bible verse or a lemma might show), the Look Up section will give me options (that's where e.g. Greek lexicons would appear in a bible). I can either look up some books directly that have that datatype, or do a Power Lookup to see all of them:

Now the Power Lookup (which usually opens at the far right of the Logos Window) gives a quick preview of all the possible resources. It will show that AT:HS comes with 16th century English (more archaic spelling etc), others, like  Creeds of the Churches, The Protestant Face of Anglicanism, The Faith We Confess, the 1662 BCP, and Anglicanism: A Reformed Catholic Tradition contain the 17th century version you called "modern english" and one, Theology of the English Reformers, even contains a present-day English paraphrase:  

You can open the books from here, and if you like a specific version, you can prioritize that book and in the future, the links should show the version you want. 

Hope this helps!

Ah, this is exactly what I needed!  Thank you so much

Glad to hear that!