Using the hint to lock READPAST is correct and your SQL looks fine.
I would add the use of XLOCK, although this is also HOLDLOCK / SERIALIZABLE
... [MyRecords] WITH (READPAST, ROWLOCK, XLOCK) ...
This means that you get the identifier and exclusively block this line during its transfer and update.
Edit: Add the index to the Sent and Received columns to make it faster. If [ID] (I assume PK) is not clustered, INCLUDE [ID]. And filter the index too, because it is SQL 2008
You can also use this construct, which does everything all at once without XLOCK or HOLDLOCK
UPDATE MyRecords SET
UPDATE, assign, install in one
gbn
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