Were to get fuse box for dedicated line?

The reason you're having a problem finding a load center type fuse box is because (I'm pretty sure) they're not made anymore - they're sort of like NOS, surplus only.

Where are you going to grab the power for your fuse box? If it's from the main house panel, then the feeder wire from the main panel to the fuse box has to be protected; the only way to do that is to install a new breaker for this feeder. You can't run an unprotected wire outside the panel, if you do, your fuse box becomes meaningless. If you have to use this breaker, then why not just make it a circuit instead - less devices along the power path. Either way, I would check with the local building department to cover yourself.

Actually there IS another way. My old farmhouse has two fuse panels, because the original wasn't large enough to accomodate the additional circuits which were added later. The licensed electrical contractor who performed the add-on installation simply added the 2nd panel in parallel to the original. This was done by (first de-enegrizing the mains at the meter pole) loosening the large screwdown lugs where the mains connect to the original house panel, then adding additional large conductors to those lug connections & running them a very short distance over to the 2nd fuse panel immediately next to it. The two panels are simply adjoined with a short conduit-type pipe connector within which the interconnecting "feeder conductors" are contained. Those #4 awg feeders are protected by the same device which protects the incoming mains, which is the service pole disconnect.
The confusing part for me to understand is that at the meter pole there is a huge *circuit breaker* which protects those incoming feeders, so yes, the power must first flow through that device. Why a smaller ckt. breaker downline (vs. a fuse which reportedly sounds better) makes any difference I do not know. But fuses are arguably better protectors than circuit breakers are, according to what I was taught in a motor-protection course that I once attended. Just to be clear, I never made the (breaker vs. fuse) sonic comparison myself; Redkiwi did perform that test & reported his findings here long ago so I am not arguing that point. My own testing involved comparing a glass fuse with a ceramic fuse, which Redkiwi & some others before me reported ceramic to be the best sounding & I do agree based upon my own results. I have never tried a breaker for comparison sake because of course my panel doesn't accomodate breakers. We suspected that the difference may be due to the fuse comprising one continuous internal path, vs. a breaker's internal switch contact which is of course not continuous, but I do not actually know the reason why. Thus Hdm's above report seems contradictory to that assumption, & so there may obviously be some other contributing factors of which we are unaware.
Within the realm of circuit breakers themselves, there are the standard models & also the GFI models. The ground fault breakers are reported to sound the worse of the two but again I don't know the reason why, I only know of the reported test results.

I would suggest you consider only one dedicated outlet, as having several gets the gear on the separate outlets seeing different phase angles of the 6o cycle waveform. The best method is to get a power conditioner of sufficient wattage to handle all your gear, for both clean power and phase angle issues.

Fuses vs Breakers. Well I don't know about sonic differences, but as to protection here's something to think about. A tree next to my house was hit by a very strong lightning bolt, which came underground into my house doing damage to all the TV's, VCR's, Microwave, Refrigerator control panel, Computer modem. My audio stuff (dedicated line with old fashoned fuse)was unscathed!
In my old house I had at that time a mix of fuses and circuit breakers. Almost every fuse, of every kind was blown. Not a single breaker opened.
The insurance adjuster told me that the insurance companies have forced fuses to be replaced by breakers, not because breakers work any better, but because people quite commonly put pennies under blown fuses! They really did that. I thought it was just a joke.

I'd like to rescind my post above. This thread put me back into experimentation mode this morning and I removed the "mini-breaker" type fuse and replaced it with a standard plastic. They do sound quite different. But I've come to the conclusion this morning that the "mini-breaker" was rolling off the highs as well as being inaccurate in that area, leading to a perception of being smoother. But the standard fuse is definitely more accurate and extended (possibly not a great thing with bad digital recordings). My tv is on a separate circuit and I was running a mini-breaker on that as well, which I replaced with a standard plastic, which in turn confirmed my findings on the audio side by offering up a slightly better picture.