Note: I am neither a lawyer nor a financial adviser. This is neither legal nor financial advice.
TL;DR: In this situation, you have to file an FBAR (but, apart from the hassle of doing so, this should not cause any problems).
The full PDF of the instructions you link can be found at BSA Electronic Filing Requirements For Report of Foreign Bank and Financial Accounts (FinCEN Form 114).
Despite the "General Instructions" section including:
Who Must File an FBAR. A United States person that has a financial interest in or signature authority over foreign financial accounts must file an FBAR if the aggregate value of the foreign financial accounts exceeds $10,000 at any time during the calendar year. See General Definitions, to determine who is a United States person.
The actual step-by-step instructions (starting on page 10 of the PDF) state:
Step 1. Determine the maximum value of each account (in the currency of that account) during the calendar year being reported. The maximum value of an account is a reasonable approximation of the greatest value of currency or nonmonetary assets in the account during the calendar year. [...] if the filer had a financial interest in more than one account, each account must be valued separately.
and then continue:
If the maximum account value of a single account or aggregate of the maximum account
values of multiple accounts exceeds $10,000, an FBAR must be filed. An FBAR is not required to be filed if the person did not have $10,000 of maximum value or aggregate maximum value in foreign financial accounts at any time during the calendar year.
Together, these mean that, for example, $6,000 transferred from one foreign account to another will contribute to the "maximum value of each account during the calendar year being reported" for both accounts. The instructions do not seem to take such transfers into account (indeed, the word "transfer" is not present in the document).
This view is seconded by the article How to Determine Maximum Annual Account Balance for FBAR on the Taxes for Expats website. That article seems tailor-made for your situation, posing (and answering) the question:
I have transferred funds between accounts; do these balances get counted twice?
Simply put, yes.
But don’t be too concerned. It is understandable if you don’t want to appear to have more assets than you actually have, but the government is not going to give you extra scrutiny for the differences between USD 550,000 and USD 700,000. The US Department of the Treasury is aware that transfers can cause funds to be double counted.
The regulations require you to report “the maximum account value of each account” within the timespan of the FBAR reporting period. Notice that there is no reference to tieing out the balances to the total worth.
So, not only do you not need to adjust your balances to avoid double counting, but in reality it is not the correct way to do it. It is the maximum account balance of each account that must be reported.
It then notes:
FBAR is purely an informational form and there is no tax assessed on the amounts reported. Therefore, reporting the transferred funds twice does not have any financial consequences.
So, the only downside of the US Treasury not taking transferred money into account is some extra form-filling.