Love the way you are thinking GR
,
Here's a ramble of thoughts for you...
porchfiddler mentions above a step mash. Such a mash is said to give you a more attenuating, drier wort. It's probably true but the more I read and learn, the less I trust what I read and learn. There are many reasons for this.
You are contemplating a 'mini' reverse of this - starting high and then dropping a few degrees. This is what happens in most 'pump-less' traditional brews but temp differentials are more pronounced there as well. Not sure what we can learn from this? (see Experimenting, Investing and Wool below
)
mally mentioned above about moving this thread to the research section. It would certainly be a good place for it but I think BIABrewer is still trying to come up with a good structure for that forum. For example, this thread should probably be in a section of that forum called, "Can this myth be busted?" or, "Would we learn anything from this experiment?" How do you word or structure that?
Experimenting, Investing and Wool 
Let's think of experimenting the same way as we do as investing. In other words, we look at the risk/reward ratio. In brewing experiments we risk our time and effort hoping we are rewarded in knowledge. In this case, we are asking whether we should invest in this stock (temp control) or that stock (no temp control). That's a fair enough question, for sure.
But, if I buy stock A today and see how it fares after 4 weeks and then buy stock B and see how it fares after 4 weeks, I have learned nothing as market conditions (water, palate etc) will be different. Unless I buy those stocks at the same time (brew them side by side) I really won't know which one was the better stock.
Let's pretend that you can buy those stocks at the same time (even though most brewers can't). A market requires a group of people to set the price (quality). Any market price is a summary of subjective opinions. (Greasy wool might be great for the candle stick maker but not for the yarn spinner). Grease content, like specific gravity, is fairly easy to measure with the correct instrumentation (often dodgy for brewers) and quantity (totally lacking for home brewers) of wool.
So, even with things we can measure, we home brewers already have a problem.
GuingesRock has written a great post above (#15). I really like the thinking that has gone into it. I think though what GR really wants the answer to is point 6 of his post, "Comment on how the taste compares..."
I think this is where we come up with a real problem. When classing wool, if my memory serves me correctly, there are about 12 classes we could put a fleece into. The class is affected by many things - greasiness, length, crimp, colour, foreign matter and a heap of other stuff I have forgotten now. What's the hardest thing to measure there? Colour.
Wool colour can obviously be measured, to an acceptable degree, by eye. But what if you need a much higher level of accuracy?
If you needed a higher level of accuracy for colour and had no instrumentation, you would have women categorize the colour as they are physiologically much better at categorising colour than men. For example, ask a woman the difference between pink and mauve and they will know. A lot of men won't. (I think mauve is some light bluey colour but really have no idea and have probably spelt it wrong as well
. There you go!)
What's my point?
I think some experiments actually can't be done by us and also that heaps can. My thinking is that GR's experiment is too ambitious for now at least. We are not only unable to buy the stocks at the same time but we also have no 'women' available to tell us whether that stock ended up being 2.0 cents or 2.05 cents after four weeks.
And that's the point.
I think the experiments we take on here, at least initially, need to focus on the most easily measured factors in brewing. For example, we still need more numbers to actually answer the very basic question, "How much more efficient is a 90 minute mash than a 60 minute mash and a 30 minute mash?" That's the easiest experiment of all and it is still very hard to collect enough solid data to make conclusions we can all trust.
This experiment game is a real thinking game (for me anyway). I think it involves thinking up and posing a lot of questions (like GR has done here), challenging them, discarding some, keeping and refining others and so on. Sometimes that is easy and sometimes it's very tedious. Humour and frustration nearly always play a valuable role. At the end of the day, correctly formulated questions are the key, the distillation of all these things.
At the end of the day, I think we also have to realise that there are some answers we'll never be able to determine for ourselves. Like women with colour, some brewers just have a knack for knowing how to 'fine-tune' a beer in a certain area. Why bother with the fine-tuning though when we still haven't built a robust aerial?
PP
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