A family of Microsoft relational database management systems designed for ease of use.
Please use precise language. You did not gain an additional database, but an additional table. That seems to be a side effect of changes to the SP list:
http://kbasrai.com/b/2013/04/17/taxonomy-hidden-list
It appears you don't want to change any field, but want to change values in existing fields. This is called offline editing.
As a test I would try exporting a new simple SP list. Can you still edit? I assume yes.
Then maybe I would conclude that the taxonomy fields are too much for Access to handle and you can no longer edit this list.
Maybe you can export to Excel and edit in it?