The determining factor for me is the overall strength of the rearends in these cars. I have built several '55s and a '56 priour to the '57 I now have. '55 and '56 had weak axles and rear wheel bearings. I wiped out several right rear wheel bearings and twisted a couple of right rear axle shafts in my '55s and my '56 before changing out the rearends for stronger units.
'57 had stronger axles and larger/stronger wheel bearings compared to '55 - '56 but '58-up wheel bearings are stronger than '57 and there were upgrades to 3rd members from '59 through '64 as vehicle weight and horsepower increased.
In my experience, 300 HP (measured at the flywheel) is the max I would consider putting through a stock '55 - '56 rearend and that would be with the understanding that stock wheel bearings would not last as long and I would definitely paint a white stripe down the length of at least the right axle shaft and pull it from time to time to check for twisting.
A stock '57 rearend, I would trust to take around 350 HP under the same conditions except I would not worry as much about rear wheel bearings and twisting axle shafts.
That said...... All my '55s, my '56 and my current '57 have been stick shift cars. I have never owned one of these cars with an slush box and never intend to so long as my left knee doesn't go out entirely. If I were running an automatic, I would up the max HP (measured at flywheel) that I would trust a stock rearend to handle by 25 - 30 HP because of the power lost to operate an automatic and the 7 - 8% power loss through slippage when not in high gear with converter locked up. And unless you have what I would call a race only 'shift kit' that slams an automatic transmission into gear (shocks the driveline) unnecessarily with each shift...... Automatics are generally easier on driveshafts, U-joints and rearends than are stickshifts.
My rough rule of thumb has been to swap in a stronger rear (9" Ford/12-bolt Chevy/9-1/4" Olds/8-3/4" MOPAR) in these cars for any engine exceeding 400 HP and/or 400 ft./lb. of torque.
The exception would be if I decide to beef up the rear in my current '57 (I anticipate right at 400 HP from the small block engine I am putting together now). In that case, I would look at beefing up the stock '57 rearend with an early '60s posi 3rd member, stronger Moser axle shafts and add your '58 - '64 big bearing kit. And since I have always built my cars to handle well in turns, the added strength (rigidity) of your wheel bearing retainer would be a plus for me as far as keeping the axle shafts and rear wheel bearings from moving laterally during hard cornering. I will be in touch when I reach that point.
Thanks,
Harry