The proper way to do it with paket would be:

* get rid of the Dependencies project (it was a side effect of trying to cope with the pain of using raw nuget)

* add a paket.dependencies at the root of your repository listing all nugets used across the solutions

* next to each project, add a paket.references file with the names of the dependencies (only top level, you don't need to list transitive ones)

running the convert-from-nuget command should practically work out of the box if you don't have far out inconsistencies (which I believe you managed by reducing amount of packages.config files), but I'd recommend to do another round of sanitization similar to what I'm describing.

I think if you give it half a day of studying / using paket on a smaller repository, you'll figure out all the things you need to accomplish migration on a large scale repository, after which you'll be recouping benefits any time you need to adjust references in projects / add or update nuget packages.