About the output inductor and caps, as has been pointed out, they are in the feedback loop, so whatever nonlinearity they exhibit should be attenuated (not eliminated) by feedback. The caps are just a high frequency shunt to ground, so I am not much worried about them. At < 20 kHz, the impedance of the coil is still low, and there is plenty of loop gain to correct anything they do. Replacing them in a way that they are twice as high could also be called making a bigger antenna...
The output coil probably uses the ferrite core and cage mainly for EMI screening. The inductivity enhancing effect of the ferrite is probably not much needed here, as a pure air coil is similarly small (20 mm dia., 20 m length and 27 turns will give you 10). Using a large copper foil inductor is a bad idea for several reasons:
- again, it is physically huge, meaning it acts as a radiating and receiving antenna
- there will be a strong magnetic field from the coil axially
- the copper foil design has a much higher shunt capacity than a single layer, solid wire air core inductor, meaning it does not do its job of attenuating HF switching noise properly.
Since the existing ferrite core is probably not magnetized much, I wouldn't worry so much about its nonlinearity as a function of current. However, purists might be afraid of Barkhausen noise that, similar to Class B crossover distortion, will be highest when the magnetization of the core switches from one orientation to the other. So if one really wanted to use an air core inductor, a single layer air core toroidal is what I would try.
About the unidirectional fuse, I am still speechless. There is nothing in the cited notes from the manufacturer to indicate that the construction is directional, nor does AC current have a direction. There is a small effect I might concede: I did measurements on a SMPS1200
https://www.diyaudio.com/community/threads/hypex-smps1200a400-measurements.358972/, and there is quite a bit of rectified 50 Hz noise evident on the secondary. Getting rid of one of two fuses in series or using a low resistance fuse will slightly change this noise, but changing your power cord or using a different outlet in your house will too. Actually, lower resistance is potentially worse here.