Hey jlua.
I've been searching for a similar problem (8 gb .pst, company was acquired, moved from 50gb mailbox to 2gb mailbox, use 2 laptops, virtual machine for windows 10, and I like having my mail wherever I work. )
So here's my thoughts, and nothing is ideal, so let me preface with that.
I'm going to solve my problem by moving my older mail to a "cold storage"-i.e., because it doesn't get changed that much, I will put the main copy on onedrive, and then keep local copies on all of my devices -- because you can't have Outlook accessing a
.PST on onedrive, its a recipe for getting corrupted. If I get around to it, I would set up some sort of intelligent (differential) copy at the 8pm or so every day to the onedrive folder, because I usually am not working on two different machines in a given
day, and that would keep everything in sync.
Then, when I logged in, I would have a process run a similar differential copy to update the local copy.
Honestly though, that sounds like overkill because all of the mail in the PST is from last year, I can likely just have it backed up with local copies. When I decide to backup more mail, I will just repeat all the copying.
Solves my problem.
Now coming to your issue. You certainly could do something similar for older mails, and have a decent sized PST you are carrying around with you. However, I wouldn't do that.
Create a backup of your .PST (create a new PST, copy all your mail to that). Drag and drop your folders.
Delete your email from gmail in the Outlook client.
Now go onto your gmail (in the web client) and delete all of your email.
Disconnect Outlook from your gmail as a POP connection.
Add Outlook to your gmail as a IMAP connection. No mail should download, since you deleted it all.
Copy your folders/mail back to your original gmail.
Set up IMAP for your original gmail on the other machine.
Now, moving forward, your Calendar, Email, Notes and (I believe) Tasks will be sync'd.
If you want your historical Calendar/Notes/Tasks, I am not sure if this would work. To be safe, I would follow my earlier path of putting them on a .PST in cold storage.