You are correct. We can not edit "Check #" field of an existing reminder.
However, we can set the "Check #" field of a new reminder by using an existing transaction in a register as a template for the new reminder: right-click on the transaction and select "Add Reminder".
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In my experience, using "Add Reminder" from the right-click menu is not a reliable way to get the register Num value into a Reminder. In fact, I can't find any reliable way to accomplish that.
I tested with all Quicken-defined Num list choices: "DEP" and "Print [Check]" were in the Num field of the Reminder created by "Add Reminder" - but "ATM", "EFT", "Next Check Num" and "TXFR" were not.
None of my user-defined Num list choices were ever in the Num value of a Reminder created by using "Add Reminder" in the right-click drop down.
In some cases, a Quicken-defined Num list choice is substituted for the register User-defined Num list value when creating a Reminder using Add Reminder. I used Add Reminder on a deposit transaction with a Num value of "Direct": the resulting Reminder had a Num value of "DEP".
My current test was in Q2019 R14.27. But my results agree with my recollection from multiple earlier versions of Quicken.
Other than noted above, I believe the only way to get your choice of Num list value in a transaction Entered from a Reminder is to have the Reminder "Remind you" then key the desired value in the "Method/Check" field (or select the desired value in the "Method/Check" dropdown).