@charley-b 

RE: What is the easiest way to add a non-posting, non-financial note on a single line in an estimate and invoice?

There are several ways; you've identified a couple of them.

RE: I would like to add notes that do not tie to any accounts.

That's easy.

RE: I do not want to leave them in the memo field. 

Well, you can add a note to the memo/description column in the table that is not posting and won't show up in report, though it will print. Is that what you mean by a memo field?  There's also a way to make it not print, if printing is the issue.

RE: I do not want to add them to the Statement note field

I don't know what a "statement note" is?  I don't see one on an Estimate or an Invoice.

RE: Is there a standard non-posting account in QuickBooks? 

Only the special ones for PO's and Estimates, but they won't help you add notes. How would a non-posting account help?

You can add notes to transactions using the transaction Notes feature. It looks like this:

Does this do what you want? If not, what is missing that you need?