The only parts needed are the differential side gears, they are available from Ford. The other part of the conversion is the carrier bearing size. There are two carrier bearing inside bore sizes, and two carrier bearing outside bore sizes. There are three possible combinations, small ID-small OD , large ID-small OD , and large ID-large OD. Factory 31 spline axles came with the last two bearing configurations, but not with the first. On 28 spline carriers, the axle bore on some of them are not large enough to allow the 31 spline axles to pass through.
The carriers with the large ID bearings can be bored out to use the 31 spline axles. Not a precision job, just big enough for the axle to pass through, I use a cut off end from a 31 spline axle to check when it's large enough. I takes less than an hour to do both sides, and could be done at a vocational school by a novice. The small ID bearings won't have enough material left for reliability if bored out for 31 spline axles. Also if your housing has the small axle bearings, you will have to have axles custom made, as there are no factory axles with 31 splines,and small axle bearings.
Both the large axle bearing, and the extra large axle bearing (some F150 trucks) had 31 spline factory applications. From about 1970 on, the big Fords, Mercury's, and Lincoln's has axles big enough to respline with 31 splines if they are shortened about 4- inch per side. Both 4 1/2- inch and 5- inch bolt patterns are available.
If you want to redrill to a 4 3/4- inch Chevy bolt pattern, use truck axles, as there is more room for the new pattern without hitting the other holes. The drum pilot may have to be turned down, depending on the drum used. The Chevy drums of corresponding size to the Ford brakes will fit if the pilot is turned down.
Most passenger cars, with 9-inch rear ends, have rear end ratios commonly changing from 2.47-3.00:1 (while there have been ratios ranging from 2.47-4.30:1). The Ford half-ton trucks with 9-inch rear ends commonly have ratios ranging from 2.75-3.70:1 (while there have been ratios ranging from 2.75-4.57:1). There were more truck 9-inch third members with 28-splines up to 1973, than there were after 1972. The '73 and up models tend to have 31-spline third members, although there were some 28-spline third members produced for these later 70s model half-ton pickups.
Some of these Versailles factory disc brake rear ends came with 1/2- inch bolts holding the axles to the rear end housing's end flanges, while some had the 3/8- inch bolts. These Versailles housings can be modernized with a larger (but lighter) set of disk brakes and calipers pirated from the Ford Explorers or Mercury Mountaineers!