Re-Wiring to add new main panel and make existing panel a sub
This is a feasible undertaking. You should be able to reuse the existing run from the meter and land it at the new main panel. You can also have the electrician pre-run the wires for the car charger
For the new main panel, install a panel with more spaces that you think you'll need, you already saw the result of not having enough spaces.
The biggest thing to make sure is that the current panel has it's neutral and ground completely separated when it becomes a subpanel. Many times in the main panel the grounds and neutrals will be on the same bar, but in a subpanel they must be completely isolated from each other. How easy this conversion is depends on how much slack the previous installer left on each wire.