I think that they will flip the concurrent filing rule on its ass, pretty much allow people whose priority date is not yet current to file for adjustment, that's the only process that I personally can think of which would give H4's work authorization.

Overall if they do that will cause some strange situations:
1) How it will affect CSPA - Overall filing I-485 freezes your age, this could potentially keep children who are nearing 21 to remain covered as derivatives even if they have aged out. Considering how USCIS hates CSPA we will see numerous lawsuits by such derivatives.

2) If I-140 and I-485 are pending then H-1B and H-4 visas could be allowed to expire since the I-485 will cover the applicants. Now this can cause a few problems on its own:
a) If either or both are denied then depending on how much time has passed since H-1B's expiration it could result in the applicants instantly facing a re-entry bar. (Keep in mind that time between the expiration of your status, or I-485 filing date if no status, and denial date retroactively counts as illegal presence).
b) Conflict with #1 and extension of #2a: The article talks only about spouses so there's the big question of if children will be eligible to file for adjustment prematurely. If yes, and not be eligible for work authorization, then that will conflict with law stating that applicants for adjustment are eligible for employment authorization. If not then the families would need to superfluously extend their H- visas so the child(ren) wouldn't fall out of status and subsequently not be eligible for adjustment.

Only other option I see is giving them a status similar to deferred action or parole w/ work authorization.