I think migrating to Adobe Managed App Measurement is a smart idea. The configuration you've described is most likely a legacy implementation, and with few exceptions, is not necessary. This setup also has the potential to cause issues with the implementation as it scales.
The best way to migrate is to move all "do_plugins" code to custom page code (as you've indicated) and leave the default execution settings.
If you need to migrate 3rd party tags and are concerned about load timing, I would add each tag separately as 3rd party JS (for better control and management) and then decide, based on each tag, if you will need to configure the load of the tag (top of page, asynchronous, page bottom, etc).
I agree with Mark's answer. One additional thing that you might run into is scoping on the s object. If you do, we have some workarounds that will globally scope the s object. Let me know if you run into that and I'll see if I can find the latest recommendation.