There is NO chance a new hub besides a 3 spd that will fit on that old bike.
I have those hubs, except for either 8 speed. I ride the 3 speed at 48 GI and get up 10% hills just fine.
The SA 5 and Nexus 7i have the same range. I rode them at 34 to 84 GIs for a while this spring, they do climb way better that way.
But I hate going slow and made them 38 to 92.5 GI or 46 to 110 or 115 GIs.
Coaster brakes are dumb anyway, get a SA drum brake.
The SA 8w has a 33% gap at both ends, so it's actually not great for hills. 1st gear at 35 GI, then 2nd at 45 GI or so, is higher than your low now. It is good that 1st is direct drive. This example is for 32/ 25T. One guy here uses 30/ 25T.
Shimano roller brakes are dumb for sure, with a lot of drag and heat.