- quick dislaimer: I've only done international seo for a site that had sub domains and sub folders. Never cross-domains. So take the recommendation below with that in mind.
Hey Paul,
I generally translate "equivalent" as "this page (X) is the same as page Y but in a different language or intended for a different region".
When you said, "This is being done to prevent North American pages from being served in the UK, Spain pages from being served in Portugal, or any other combination of possibilities..." I wanted to let you know that you might not need to do anything in your sitemap. I don't know exactly how you set up your domains or translations if any so I use caution with that statement. But, if one of your sites is meant for Portugal, you can set geotargeting in Search Console to accomplish this. Even if the content is the same on another site but that other site is set to a different country, you shouldn't have a problem with duplicate content. That geotargeting is basically a signal to Google that you want users in Spain to see the Spain site and people in Portugal to see the Portugal site and these two pages won't be competing.
Where you would want your href lang is on translations of those sites in the perspective countries. So let's say the Portugal site has an Portuguese, English and French version (the main languages in Portugal) then you would set alternate href lang tags for all the translations on that site. But if your site dedicated to Spain also has an English version, you wouldn't need to cross reference the Portugal site if you use geotargeting. (Hope that makes sense)
Alyda Solis, who is an associate here at Moz, has a really cool tool on her site that can help you build the syntax. https://www.aleydasolis.com/english/international-seo-tools/hreflang-tags-generator/