Do it manually, with a few preliminary steps so you don't have to create folders manually (this might save a LOT of time, depending on how extensive your project's folder structure is)
- Add the project to a PC with Connector that doesn't already have active projects.
- Copy (not move) your SOURCE data to a temp folder on your Connector PC (C:\Temp).
- Search for all files in this TEMP folder and delete them all; this will leave the folder structure behind. Windows might take a while to index, but you'll know if it's empty by right-clicking the folder->Properties and ensuring the size is 0kb.
- Copy-paste the empty folder structure (HAS TO BE EMPTY) to "Autodesk Docs" in your "Project Files" folder; this will create the empty folder structure on the web interface.
- Wait until it completes its sync (you might have to restart Connector a few times).
- Go to BIM360 web interface and drag-drop all files from the SOURCE into their proper folder in BIM360 (400 files/drag is the limit ... this has to be done folder-by-folder).
- Once this is done (all clouds or green checkmarks) restart the PC. Once restarted, give Connector a good 10 minutes then see if the folder is still all clouds or green checkmarks. Anything that is still syncing will probably need to be deleted from the web interface and re-uploaded. Repeat this step until the computer boots to a "happy" sync.
- Copy-paste your SOURCE folder to the Project Files folder. When you get the "do you want to overwrite files" hit "No to all"; this will then only make Connector need to upload files you uploaded incorrectly during your manual upload. If you can limit Connector to only having to deal with maybe 100 files, it'll probably work.
- Repeat the reboot-wait-manual upload process until you have all clouds or green checkmarks as before.
You might be tempted to directly copy-paste to Autodesk Docs. It PROBABLY won't work, and it will leave you in a situation where you have to reset Connector a bunch of times and Connector might just randomly delete files.
At that point, you will have to manually fix any XREFs that aren't working. You'll have problems if AutoCAD was previously able to find incorrect XREFs somewhere in the folder structure, but it won't be able to do it through Connector.