You would likely have to find a much later rear end to get disc brakes. In addition, many newer rear end assemblies have leaf springs so it would have to be modified. This would include welding, changing brake lines, and brake cables to adapt to your coil spring rear suspension components. Front disc brake conversions are available from a variety of aftermarket suppliers and would include an upgraded booster/master cylinder.
All of this would cost way more than $1000. While I believe the front disc brake conversion is the way to go, I would seek a second opinion from someone that specializes in rebuilding rear ends.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine