When to use (or not use) commas in a sentence with conditions

Current Sentence:

The steps in this procedure must be performed chronologically until the card has been found, or all the steps have been exhausted, and an adjustment to the system must be made.

Proposed Edit:

The steps in this procedure must be performed chronologically until the card has been found or all steps have been exhausted and an adjustment to the system must be made.

Update to my proposed edit, based on comments:

The steps in this procedure must be performed chronologically until the card has been found or until all steps have been exhausted and an adjustment to the system must be made.

My hope is that the update to my proposed edit clarifies the meaning of the sentence. But absent the second instance of the word until, what is the best way to explain this to the writer so that they have the tools to avoid the mistake in the future? (Perhaps this is a training question that is out of scope for this forum.)

(The writer has been told to follow the FANBOYS acronym when separating two independent clauses with a coordinating conjunction. So the writer went comma-crazy.)

Assuming my edit is correct that the remaining clauses in this sentence are dependent on the preposition until, is there an easy way to explain this to the writer? I’m new to editing and honestly don’t know the best way to explain this.

Thank you for your assistance.

SPECIAL NOTE: This is not a card game. 🙂 But it has been simplified to avoid the name of proprietary software.