"Faster" RAM at lower clock speeds?

Typically, you'd gain more benefit by higher MHz vs. lower CAS timings. In a general case, even though your CAS timings may be increased to 5-5-5-15 from 4-4-4-12, for example, the extra 133MHz of clock speed gained will allow the memory to go through those CAS cycles in less time, thereby being "faster" in terms of random access.

However, it seems that you've stumbled upon an edge case where the lower CAS timings take less time than the higher CAS timings, despite the lower clock speed. In theory, I suppose that a 100% random workload would perform better in this scenario if your math works out. But like others have said, there are other factors to consider (motherboard, etc.), and this would only apply for an entirely 100% random workload that only reads a single word at a time. For the case that you defined, the difference is marginal as it is. Anything aside from that hypothetical random workload would have less performance than if it were running with the RAM modules at a higher clock speed.

In the real world, when there's a tradeoff, go for the higher MHz (or registered modules, or whatever applies to your need).

So my question is: Is this in fact true that I can actually improve the performance of my system if a program I run is accessing the memory in a truly random fashion (as opposed to sequential read/writes) by under clocking the RAM and selecting a tighter timing or have I made an error somewhere?

This is hard to answer as there are many variable to consider. In theory you should be able to improve performance of just those programs. This assumes that memory is highly fragmented or you are reading/writing small amounts of data. Also note that your overall system performace may degrade. Best thing to do is give it a try as it is a very simple test assuming your BIOS provides access to those settings.

You can use the performance index described here: http://www.anandtech.com/show/7364/memory-scaling-on-haswell/10 I am not sure how it applies to low speed rams, but in your case:

333/5 = 66.6
266/4 = 66.5
200/3 = 66.7

So in theory it does not matter which settings you choose.