You can schedule this update.

Just comment out \Elgg\Upgrades\ContentOwnerSubscriptions::class, string in this file https://github.com/Elgg/Elgg/blob/5.1/engine/upgrades.php

Like Nikolai said. You can do this upgrade later.

Once you've migrated your site to 5.x you can re-enable the upgrade and run that specific upgrade in the CLI (check the params for elgg-cli upgrade). I don't know if you could run it in batches (by canceling the upgrade mid run) but most of the time these long running upgrades don't have a heavy impact on the database (you could test this). So you can have it running on the background of your live site.

Excellent -- thank you both.  This will really help simplify our migration plan.

Ok, I think I have an idea what's going on, though I'm still not sure of the root cause.

I found that if I change the access_id during an action (like the edit action of the entity in question), it works fine.  But if I change the access_id in a view, or change it when the action is invoked via AJAX, it doesn't work.

I could see why Elgg wouldn't allow access_id (or other entity properties) to be modified in views.  I'm not sure why calling my action from AJAX seems to have the same issue.

No code, no ideas ¯\_(ツ)_/¯

Hahah, fair enough.

I finally figured this out: I discovered that my entity has a canEdit() function that was returning false under some circumstances.  Those circumstances just happened to coincide with when I was attempting to call my actions via AJAX.  So the AJAX was a red herring after all.