Save & Keep Working/Required Fields

Hi all! 

I posted last week but am really stumped still. Some of my end users are requesting to save information while still working on a new record -- and in our workflow, it's common that they may be gathering datapoints over multiple hours (and sometimes in 15 minutes). They don't want to lose their datapoints as they complete collection - and we don't want to miss any of our required fields, which are critical to a number of areas from regulatory requirements to funding support.

Someone suggested that I "hide" a section that has the save button and add the conditions on that my required fields must be filled in to show that section, but the save button is actually always present, so that doesn't quite achieve what I'm hoping for.

Additionally, we have some layered requirements - if X is "Yes", then require 4 other fields. So I'm just trying to figure out the best possible approach to letting them save their progress, while not relinquishing control over getting those required fields.

Any suggestions are most graciously appreciated!