"If you, as I do, import transactions, they can be automatically marked as cleared or even reconciled, depending on the download source."

Most typically, for using QB, you see them marked as "verified" which in QB PC is a lightning bolt and I believe QB MAC is a C (cleared) and not R (reconciled). Or, as noted above:

"There are 2 types of check marks in the register. The lighter check mark is a matched transaction through online banking, the darker check mark is a reconciled transaction."

So, all of these products use different Indicators for the 2 stages of status. Verified Vs Reconciled (processed through the reconciliation tool).

"Make sure they are all uncleared before reconciling. This is a pain, as it has to be done one at a time, but my starting balance then reverted back to the correct number (the previous month's ending balance)."

In PC, the reconciliation screen has a Matched button, and you click it, and the lightning bolt transactions are changed to Cleared, and Finish the reconcile is how you end.

So, the downloaded data carries a status (no matter what the terminology is) but that is not a Reconciliation.

"No, the beginning balance is NOT the number I ended with the last time. That's the problem"

I pointed out this Value, from how you ended last time, is the Net of the DATA in your file that is marked Cleared as Reconciled. If it no longer matches, then you can run a bank report to see if there are old transactions no longer Reconciled, or newer transactions already Cleared. I was describing the Source of that value.