Yes, brakes and spindles both have to be changed. The control arms are the same for both (through 72). Then I had to change spindles again when I went from ten inch drums to SBP discs up front.
Have not tried to swap tens for nines on the rear, but actually nine inch brakes in the rear work well with discs up front (that's what I'm running in my 63 Valiant convertible). Or with ten inch drums up front, nines rear, which is what I ran in my old 66 slant six Barracuda. At least you don't have to worry about the rear brakes locking up first, which can be an issue with ten inch rear brakes, requiring either a proportioning valve or smaller brake cylinders in the back. Put the latter in my 67.
Factory could play that game, too. My 56 Plymouth Belvedere V8 was factory equipped with eleven inch drums up front, ten inch drums in the rear. (56 Furies had elevens all around, six cylinder 56 Plymouths had tens all around.) Even stranger is that my Belvedere's eleven inch front brakes have studs and lug nuts, while the ten inch rears have lug bolts that screw into the drums. And yes, that's the way it was delivered when new.
