I have a project (private, ASP.net website, password protected with https) where one of the requirements is that the user be able to enter Sql queries that will directly query t
My gut reaction is that you should focus on setting the account privileges and grants as tightly as possible. Look at your RDBMS security documentation thoroughly, there may well be features you are not familiar with that would prove helpful (e.g. Oracle's Virtual Private Database, I believe, may be useful in this kind of scenario).
In particular, your idea to "Verify (using Regex) that the user has permission to access the tables being queried/updated, included in joins, etc." sounds like you would be trying to re-implement security functionality already built into the database.