You're seeking an efficient and effective way to conduct UAT in a structured manner. I highly recommend using a pairwise or combinatorial test design approach. I have used this approach in more than 2 dozen proof of concept projects and found that, as compared to traditional methods of identifying test cases manually, this approach consistently leads to dramatically more defects being found per tester hour. In fact, on average, as reported in a recent IEEE Computer article I co-wrote, we found 2.4 X as many defects per tester hour on average.
The approach is described in the video here. Apologies if this appears to be an "use my tool" plug. I don't mean it to be. It is the approach that will deliver dramatic benefits, not the specific tool you choose to use to design your tests. James Bach also offers a free tool called AllPairs on his satisfice.com site. My point is that using any such tool will generate dramatically superior results because these tools are designed to generate maximum coverage in a minimum number of tests. They avoid repetition; in addition, they automatically identify and close potential gaps in coverage that manual test case identification methods will fail to close.
While it might be counter-intuitive that a tool like Hexawise would be able to identify (in seconds) the UAT test cases that should be run better than testers would be able to identify and document (in days), it is nevertheless true. Try it for yourself. Have one UAT tester on your team execute 20 end-to-end "black box" or "gray box" tests that are created with Hexawise and have other testers test what they usually would. I would bet good money that the tester executing the 20 Hexawise tests would find many more defects per tester hour (and would find "important" as well as "unimportant" defects).
It is a shame that these kinds of methods aren't much better known in the testing community outside of a relatively sophisticated group of testers who take the time to read books like Lee Copeland's book on test design methods. Pairwise and combinatorial methods work consistently, they deliver enormous improvements in efficiency and effectiveness, and they are quite easy for testing teams to start using immediately.
Justin (Founder of Hexawise)