Okay, folks. Time for the Dummies' Guide to Ship Powering.
To a first approximation - and this is a very rough approximation to a very complex situation - power requirements vary as displacement to the power of two-thirds and as the cube of speed. The ratio of the product of these two figures to power is known as the Admiralty Coefficient.
For Yamato, with a displacement of 69,100 tons, a speed of 27 knots and a machinery plant generating 150,000 shaft (not ship) horsepower, the Admiralty Coefficient is 221.
Turn the formula around, and we can calculate the displacement for a given speed. If we want to strip weight off the Yamato to get her to 30 knots, we need to get her down to 43,000 tons from 69,100 tons. That's a weight saving of 26,100 tons. She only carried 21,266 tons of armour, so as well as leaving off all the armour, you still need to find another 5,000 tons of weight. Losing a turret, along with the associated magazines and auxiliary machinery, might do it.
In other words, doing it requires constructing a monstrosity that would make even Jackie Fisher say "Hang on a minute..."
Getting the desired speed by increasing horsepower is a bit more feasible, only needs another 54,000 shp. Though the extra machinery weighs more and takes up more space... Going from a South Dakota to an Iowa cost 30% of displacement; getting half the speed increase out of Yamato might cost 15% of displacement. Taking us to, oh, 80,000 tons or so.
This is getting silly again. And we haven't even thought about where the fuel comes from. Maybe we'd better just send Kirishima.