Cleaning folder Sent Messages on Gmail and Mail: Solved once and for all?

Hello,

I use a Gmail account with several aliases. This account has IMAP access enabled for me to use on Mail, both on my Mac and on my iPhone.

On Mail, for years I have been moving messages that I sent and that I did not need to wait for a reply to different folders (each with a unique project name). This meant that the message no longer appeared in the folder Mail Sent: it would only appear in the folder Mail [Project Name]. In Gmail, this implied that the message would get a label [Project Name] but would stay in Gmail Sent. In this way, my Mail Sent was clean with only the messages that still required a response. Everything else was in their specific folder. By all accounts, this is normal behaviour.

Today, I enabled Gmail's Two Step Verification and my Gmail account got refreshed. This has meant that all messages that appear on my Gmail Sent, now also appear on my Mail Sent folder. In the cases in which the folder Mail [Project Name] no longer had IMAP access enabled (because it was an old project that no longer required access), the message only appears once in my Mail Sent. In the cases in which the folder Mail [Project Name] still had IMAP access enabled (because it is a project that I am still working on), the message appears twice: once in the folder Mail [Project Name] and another time on Mail Sent. No changes have taken place in Gmail: this means that messages continue to appear in Sent with their specific lables [Project Name]. From what I have gathered, this is also normal behavior.

Now, how to restore things to how they used to be? I have tried the following that seems to work and I'd like to know if anyone sees a problem of any kind.

On Mail, select the message from the folder Sent that should not be there (because it had originally been moved to a folder of the kind Mail [Project Name]) and archive it by clicking Message > Archive. On Mail, a new folder Archive will appear and the message is moved from the folder Sent to the folder Archive. On Gmail, a new label will appear: [Imap]/Archive. The message that has just been moved on Mail will now have two labels on Gmail: the original [Project Name] from when it was originally moved and the new one [Imap]/Archive. And, this is important and an apparent improvement (if this is correct): it will no longer appear on Gmail Sent.

Now, I go to the label [Imap]/Archive select the message and remove the label [Imap]/Archive only. In this way, the message now only has one label in Gmail, the original one [Project Name]. On Mail, this causes the message to disappear. The message no longer appears on Mail Sent or Gmail Sent and it only appears under the label [Project Name].

I have tried this several times on my machine with a series of test messages. I'd like to know if this works so that I can actually do this with the thousands of email that are cluttering my folder Mail Sent. Any help appreciated.

Thank you!