Thanks for all the help, folks!
I finally found 1/4-watt, 1-ohm fusible resistors from a supplier in Europe. They should be in my mailbox in about a week, hopefully.
It's weird that a part that I would have assumed to be fairly common is so hard to find in the U.S.
Have fusible resistors "gone out of style" in place of something else?
I was pretty sure I could have used a regular flameproof 1-ohm resistor for this particular circuit, but I was just paranoid enough to want to be able to use exactly the right part. Why? Well, the unit in question had undoubtedly been hit with some sort of voltage surge, causing several other power supply components to fry.
Those other components have been replaced, and the deck's power supply has been stable so far. However, this latest component failure, in a very low-voltage circuit that is completely unrelated to the previously-repaired circuits, shows me that there could be other weakened components hiding just about anywhere--so I might as well re- install ALL of the original protective elements and keep a watchful eye until I am convinced the deck is completely rehabilitated.