It seems Yamamoto did consider sending his super BBs to Guadalcanal after criticisms by the IJA that the IJN wasn't doing enough, but misgivings saw an end to whatever very tenuous plans there may have been on that score. He was well aware of the speed and fuel issues and was very reluctant to send them in.
However, during my gaming sessions (using a tweaked version of
Seekrieg 5), I have indeed done this scenario as part of an AH project which saw some earlier changes to events. I used
Musashi in one scenario due to the fact in previous gaming scenarios,
Yamato had been damaged by submarine attack and was being repaired, and other BBs were also unavailable due to various reasons, therefore forcing her use despite the various concerns. Thus the scenario was only possible due to various circumstances that happened before it and didn't exist OTL. The scenario was gamed a number of times to see what would happen. It usually resulted in a vicious night battle with both sides coming out with varying degrees of bruising.
The result of the most favourable game out of this scenario in terms of damage done to the USN was she was heavily damaged, practically a mission kill, and although she struggled back, wound up in dock for around a year.
Washington was the only BB present in this situation due to
South Dakota having an earlier run in with
Hiei and
Kirishima, and having to withdraw for repairs after suffering heavy damage.
Hiei was sunk and
Kirishima seriously damaged in that battle, although
Washington only suffered very light damage. In the
Musashi battle,
Washington was sunk, but the close range fight,
Washington's radar directed hits, confined waters and torpedo attacks saw
Musashi take a beating. It was a confused night action.
Musashi's better amour on her secondaries compared to
Yamato at least helped out a little in that battle to an extent though.
So the likely result is a battered superdreadnought with a load of fuel used up, and the long term result not actually helping the war effort much. It's not impossible a better tactical result could have been gained with her suffering less damage, but that's still not going to alter the big picture hugely. At least the IJA would have been somewhat mollified though, which I'm sure the IJN would have felt it was worth it (not).
As an aside, this causes me to remember there was an AH challenge years ago where the OP wanted us to get all four
Iowa class BBs sunk up to the present day. I was going to post my AH gaming results in that one (real life intervened though and I failed to post anything), but even my gaming scenarios didn't manage to sink them all in WW2, and it was up to the post war period to accomplish that elsewhere.
I did manage to write up a whole AH Pacific War using various gamed scenarios although only my AH Battle of Leyte Gulf has been put on the net. Despite some better (or luckier?) results, the Japanese still lose the war though, as is to be expected.
Regarding Lundgren's book. He is well known over at various boards for his various contributions at
combinedfleet.com, and also at
warships1 (can't believe how many years have passed since I first participated there). His book is an interesting and persuasive minute-by-minute read using logical analysis, ship's logs, action reports, and photographs/film stills from the battle to match things up, although it does have some issues. Rather dry as noted above, though.
Sargon