Magic 8 Ball says: "Outlook not so good"
Meaning, if there were a list of 386SX machines to do this to, I would put this near the bottom.
Reasoning: Where sources gush that IBM had to pioneer a whole new RF screening approach for this machine, I think "So, it is inherently noisier than contemporary machines, such that it required extreme measures to counteract, why is it putting so much power into making noise???" So there may be deficiencies in the design of the motherboard already, components are also noisier when used at the limit of their specifications, maybe that is a factor too. Thus, it would worry me to try to get this motherboard to go faster.
Also these machines were recalled for burning holes in themselves, so yeah, like I said, probable deficiencies in design.
Then we have the IBM being IBM stuff like timing checks in the BIOS that will need to be patched out. They swear up and down that this wasn't to prevent upgrading, but to provide a check against risk of data corruption due to clocks going out of spec. More like they were deathly afraid of missing a service charge opportunity, but anyway, makes for an obstacle. The instructions for patching around the check on one of the PS/2 machines are given in Upgrading and Repairing PCs, so you'll have to adapt that.
So then there's the known unknowns like did IBM do anything else particularly devious elsewhere in the system, by now they weren't in a computer for everyman mode, but a put thumbscrews to the profit fairy mode. Then the unknown unknowns of whatever wild shit Murphy throws in your way, guess that's the same for many a modification though.
Anyway, unless you can find a mailing list that knows these inside out and has 40 page arguments about the benefits of using a 74ALS vs a 74F chip in a particular location, then chances are slim that it will be easy to accomplish.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.