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I could not find bunkerage for a DD, but it obviously would be much smaller than that for a BB.

I imagine the Navy worked out how best to do UNREP, duh.  It is interesting.  Iowa class cruising range:

9,600 miles (15,000 km) @ 25 knots (46 km/h); 16,600 miles (27,000 km) @ 15 knots (28 km/h)

25 knots is not flank of course, which is 33 knots.  That is about 700 miles (statute) in 24 hours at 25 knots, so they can maintain 25 knots for two weeks.

Here's some data for the Fletcher-class destroyers of WWII.

Type:	Destroyer
Displacement:	2,050 tons (standard) 2,500 tons (full load)
Length:	376.5 ft (114.8 m)
Beam:	39.5 ft (12.0 m)
Draft:	17.5 ft (5.3 m)
Propulsion:	60,000 shp (45 MW); 4 oil-fired boilers; 2 geared steam turbines; 2 screws
Speed:	36.5 knots (67.6 km/h; 42.0 mph)
Range:	5,500 miles at 15 knots (8,850 km at 28 km/h) [2]
Complement:	329 officers and men
Armament:	Varied; see Armament section

No info there on how much fuel it carried.
I doubt there's ever been a navy that was so big, fighting over such vast spaces, doing so many things so well, as the U.S. Navy in World War II.

EDIT: Here's info from the National Park Service regarding the USS Kidd (DD-661) of the Fletcher class.

Name:	USS Kidd (DD-661)
Location:	Adjacent to Mississippi River levee near Old State Capitol, Baton Rouge, Louisiana
Owner:	State of Louisina, Louisiana Naval War Memorial Commission
Condition:	Excellent, unaltered
Displacement:	2,325 tons standard / 2,924 tons full load
Length:	376 feet
Width:	40 feet
Machinery:	2-shaft General Electric Turbines, 4-Babcock & Wilcox Boilers
Fuel Oil Capacity:	492 tons
Maximum Speed:	35 knots
Armament:	Five 5-inch/35 caliber guns, 10 torpedo tubes, depth charges, and various combinations of antiaircraft guns.
Crew:	273 wartime
Builder:	Federal Shipbuilding and Drydock Company, Kearny, New Jersey
Launched:	February 28, 1943
Commissioned:	April 23, 1943

So, bunker capacity was 492 tons.

Coincidentally, I landed an OH-58 aboard USS Kidd (DDG-993) off of Grenada.  I took the Exec and Surgeon on a little reconnaissance/sight-seeing trip of the island while my copilot stayed on board and bought up a bunch of stuff in the ship's store.

http://destroyerhistory.org/fletcherclass/

Looks like about 500 tons of fuel oil, a significant portion of their actual displacement fully loaded.  

Yeah, I posted while you were editing.

I'm rather amazed by that.  So, if an Iowa class has 7500 tons when full, refueling a DD would put a big dent in that in actuality.

Lack of AOs was a major problem for the IJN of course (in addition to not having enough refined oil to fill them).  Later in the war, some major IJN ships used unrefined petroleum which includes the volatiles, akin to gasoline.  Not good to have in a battle.

The US Navy of course made mistakes, they are inevitable in war.  But the Japanese could not afford to make any or have any bad luck.

The Yamato and Musashi were wasted expenditures for them.  The Germans wasted a lot of effort on a nearly complete aircraft carrier.  They couldn't afford a misstep either.

Lack of AOs was a major problem for the IJN of course (in addition to not having enough refined oil to fill them).  Later in the war, some major IJN ships used unrefined petroleum which includes the volatiles, akin to gasoline.  Not good to have in a battle.

The US Navy of course made mistakes, they are inevitable in war.  But the Japanese could not afford to make any or have any bad luck.

The Yamato and Musashi were wasted expenditures for them.  The Germans wasted a lot of effort on a nearly complete aircraft carrier.  They couldn't afford a misstep either.

In both cases, their critical missteps began with starting the war in the 1st place.
With each victory, starting with his diplomatic triumph at Munich, Hitler added new enemies.  He underestimated British resolve and the USSR's ability to swallow his armies.  He underestimated us, exulting after Pearl Harbor that victory was assured because the Japanese hadn't lost a war in all their 3,000 years of existence.
Japan underestimated us, thinking we were soft and would quit after a few shots to the solar plexus.
Both of them went to war without economies that could sustain a long fight.
So, as you imply, they had to be perfect.  To make no mistakes.  They had no margin for error.
But everybody makes mistakes in war, because the enemy is interactive and often does not cooperate by reacting as it is wished that he would.

The Japanese were in a bind once we cut their oil supply.  Their generals in China were not under central control.  So, the idea they could have simply pulled back from China was not realistic for them.  They had a very short supply of oil for their economy.  The oil fields in SE Asia were there for the taking, but the US had kept the PI from 1900 that was astride their supply line.

So, what could they do realistically?

Go back in time and not invade China in the first place.  Be satisfied with control of Manchuria (Manchukuo).
As for what could they have done from the summer of 1941 onward?  Probably nothing that their national character and aspirations would have permitted.  They were committed to aggressive expansion and we were in their way.

It's interesting to suppose what might have become of Hitler had he not invaded the USSR.  (That of course was his whole reason for being, so it's illogical in a way.)

With fairly modest effort, he could have reinforced the Afrika Korps to the point it would have driven the British out of the Med.  That would have opened up the oil fields for the taking.  He was getting raw materials from Stalin in significant quantities.  He had the Baltic locked up.  He probably could have starved GB to the point Churchill would have lost favor.  The Third Reich might be there today.