Of all the ideas in this thread, this seemed the most likely to end up with a broken logic board. So naturally I had to try it!
First, for anyone new to mucking about with the Mac Pro heatsink, you need a long 2.5mm Allen key. Use it to loosen the five screws holding down the heatsink (you can't lose the screws, so just go until it stops spinning easily):
View attachment 773471
The IOH/chipset heatsink sits under the main heatsink, so you can see why the BOOSTA fan setting can greatly affect the chipset temperature:
View attachment 773476
The spring rivets in question are circled here:
View attachment 773472
First remove the standoff screws:
View attachment 773474
and you can see the backside of the logic board where the rivets stick out:
View attachment 773475
Now, I may have gotten some later-manufactured model or the original owner wasn't too hard on the Mac Pro, but my rivets were actually in great shape. I had to clip them with scissors for the purpose of this tutorial/my curiosity.
Wipe off the grease from the CPU and chipset heatsinks, and from the CPU and IOH chipset. I know some people use industrial degreasers and fancy arctic silver removal whatevers, but I've used a paper towel, Q-tips, and rubbing alcohol since I was mucking around with lidless AMD Athlons and Slot I Pentium IIs so it'll be fine here. Anyway, it should look kinda like this when you're done:
View attachment 773477
Then apply new heatsink grease to both the IOH chipset and the CPU. You do NOT need to apply it to the actual heatsinks.
Now stick one zip tie through one hole and another through the second hole, and lock them together. It'll look stupid and like it couldn't possibly work, but don't knock it till you try it...
View attachment 773478
(clip the excess zip tie like twerpin said)
Here's the funny thing - all this malarkey actually lowered my CPU/IOH temperatures. My CPU diode usually hovers around 70-80C under load (this is after already changing the CPU heatsink grease once), and the IOH diode anywhere from 70C-90C depending on how aggressively I set the BOOSTA fan.
Here's the temperatures under load (handbrake x265 encode), and all automatic fan control:
View attachment 773470
Setting the exhaust/intake/boostA profiles more aggressively (CPU diode, min/max 50C/90C) only lowers the temps a few more degrees:
View attachment 773469
So I'm guessing most of the benefit is cleaning out the 10-year-old heatsink grease that the Mac Pro originally shipped with. Anyway, wouldn't recommend doing this unless you absolutely have to. Even 70-80C is well within the tolerances for the chipset.
That said, I was able to turn down all of the fan settings in Mac Fan Control, so my Mac is even quieter than before!