BRC
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The date you initiated the payment is really all that mat...

The date you initiated the payment is really all that matters.  The download should work fine to match a check dated a few days after the one in QB.  That is the normal way banking works (checks written clear later.)

There's no issue with reconciliation.  Check off the items that cleared the bank, on the statement, and leave the other's unchecked.  That's all there is to the reconciliation.  The month or year does not matter.