Sony XA5400ES fuse directionality...

You were able to consistently measure such low resistance? What kind of meter are you using?

This is how littlefuse approaches fuse resistivity:
http://www.littelfuse.com/data/en/Technical_Articles/TB98-004.pdf

Here is the data for a 2ag, 5 amp fuse, which should be in the 'normal' range for power supplies of larger amps.
NOTE: resistance, measured cold, is <.02 ohms.

http://www.littelfuse.com/products/Fuses/2AG+(5x15mm)/208/0208005..html

Now, I have a cheap-o meter which is of low resolution. I'd like the bench meter I had at work years ago which had 8 or 9 digits of resolution.

My meter tests out to 4 digits, and it was quite a significant difference. Here is a test done by HiFi Test magazine in the same fuses:
Measuring technique: If there is a marked difference in the listening test, you should be able to measure it, or so I thought. However,
I could not measure any differences with our measuring station - neither in the frequency response, nor in the distortion response, nor in
the pink-noise – except in one aspect., - During the measurement of the damping factor of our integrated amplifier test candidate using
the Supreme3 fuses, the damping factor increased from around 350 to 500. (Reminder: The damping factor is a measurement of the
internal resistance of the amplifier and usually reveals something about its‘ control over connected speakers; the higher the damping
factor, the higher the control – at least in theory.) But here I had clear proof of the effect of the damping factor, e.g. the substituted microfuse,
on the sound. How could this be? To find out, we devised an elaborate new measuring system, to analyze the electrical properties
of the fuse.. We measured the voltage drop over the fuse (see measurement diagram), which is three times lower in a Supreme3 than in
a standard fuse. Significantly more voltage is lost at a higher current flow through the standard fuse, which is then no longer available to
the amplifier circuit.. The result would have to be dynamic loss and slower impulse response, which we experienced in the listening test.
The Berlin HiFi-Tuning manufacturer’s own explanation reads slightly peculiar for non-techies, because his explanation is a cryogenic
treatment (ultra-deep cooling) and 24-hour quantum-level treatment. What convinced us much more is the use of special silver/gold fuse
wires and a complex soldering of the fuse wire with the head cap made of fine silver. This would explain the lower electrical resistance of
the Supreme3 fuse that we measured., For example, a 250 mA fuse measured at around 1.2 Ohm (as opposed to 3.5 Ohm for a
standard fuse). It is also possible that the polyolephine wrapping of the fuse element (known as shrink tubing) is a sonically effective
"trick" of the manufacturer for resonance suppression; however, we couldn’t determine the difference "with and without" without
destroying the fuse.

I hear better when the moon is full.

Are you talking damping factor change for a power supply fuse or in the protection part of the output?
One makes a little sense, the other none at all.
Sine the max current draw is isolated from the output by (presumably) a fair amount of capactitance and the max draw thru the fuse is during 'recharge' that is a little......strange.

What is the alloy of the fuse in question. I believe Littlefuse uses a Zinc alloy which this test beforehand so they get the final fuse resistivity correct per amperage.

I've used test equipment called a 4-point probe. 2 tips used to force a voltage, the other 2 tips used to measure. VERY precise readings of resistivity are possible by this method. Repeatable and process capable (in the most rigorous technical sense) such a metrology tool is used in the semiconductor industry for process evaluation.

Wouldn't wrapping the fuse element in ANYTHING result in it changing the characteristics of the fuse?

I have suggested, in the past, a test to be used for microphonics. Put the test piece in an enclosure with a speaker. Have the same circuit OUTSIDE the enclosure. Using a dual trace scope, do with / without sound subtraction of the signal. Microphonic effects should show up very easily.