In the end you don't propose changing the tech at all only the procedure for getting the data (the law). It's not a bad idea to be honest.
In my opinion the problem is the mass surveillance of Americans in the first place. End that, and suddenly they can't look into their co-worker's lives or stalk women. They'd only have foreign intelligence information available. You'd also get the benefit of government upholding the people's constitutional rights for a change.
I feel like the real problem is the technology, the law, and the (lack of) enforcement of the law. Every one of these violations should have resulted in a criminal prosecution for a variety of criminal offenses against the government agents who illegally used these databases. Every American who was the subject of one of these illegal searches had their Constitutional rights violated. Neglecting to prosecute government agents who clearly and deliberately violate the law and the Constitution makes a mockery of our entire system of "justice".
That part can be solved with technology by requiring multiple approvals for access to data so no one agent can't look up his girlfriend (or be bribed to look up information by a private investigator) unless he can convince his supervisor (or an audit department) that person is related to some active investigation.
It's not a perfect solution, but it's the right kind of bureaucratic quagmire to actually make a difference.
Here's my fix: put the systems under the control of the Judicial branch. This way, Intelligence is not asking for permission, they are asking for access. The tech who does the search is going to answer to the branch of government that cares about the law rather than the branch of government that has the conflicts which create the rush to misuse the systems.