This sounds like a great project and something you may want to share with the community with lessons learned.
As for your question, would it be possible to do a backup/restore each day and work from the backup? I can't speak to how much calls outside tableau are going to impact the Postgres db performance. If they are simple select * then I wouldn't imagine much of a hit. Indexes, Joins, and size of the tables will all play a role not to mention the impact of your network. If it was my Server, I would probably have folks interested in access to the Postgres DB access the backup restored on a separate server to be 100% sure that no accidental drop or insert commands occur.