You don't mention if it's a steel or aluminum back rim. If it's steel, that's probably a lot of the problem by itself.

Step-through and mixte bikes with "upside-down" routing to a sidepull brake don't need special brakes or adaptors. They need a brake where the housing stop and cable anchor positions interchange, which is common on basic single-pivot sidepulls. Typically this will be a type where the housing stop looks like this:

And the cable anchor looks like this:

It can be hard to make out in the photos, but the part that passes through the brake arm on each is a flatted oval type shape. It's the same on both so they can interchange. This is a standard of sorts that's been around a long time, such that generic replacement parts like the pictured ones exist and are common shop items.

Single pivot sidepulls are some of the weakest of all rim brakes. There are some double pivot calipers that can have their position switched in the same way. You're basically looking for ones that have the kind of housing stop and cable anchor pictured. There are some in Dia-Compe's line. I think this could be a good place to look. Be careful that whatever you get has a pivot bolt that matches the needs of the frame. Specifically, this bike likely can't take a recessed nut brake, and some of what you'll find is recessed nut only, but you may be able to circumvent that by using a front in the rear or switching pivot bolts).

Upside-down routing always has the disadvantage of the housing being open to the elements in a way where gravity is working in favor of water/dirt ingress. There are various nosed ferrule and boot type products that have attempted to address this - see Brompton brakes for an example. Another approach is to just switch the routing to continuous, zip tie it up the seat tube and then back down, and use one of the various fancy compressionless housing options that will take the extra bends without adding a lot of friction. Then you could use whatever dual pivot brake you want of the appropriate reach and mounting type, which is likely the path to getting the most power you can in the application.

You don't mention if it's a steel or aluminum back rim. If it's steel, that's probably a lot of the problem by itself.

Step-through and mixte bikes with "upside-down" routing to a sidepull brake don't need special brakes or adaptors. They need a brake where the housing stop and cable anchor positions interchange, which is common on basic single-pivot sidepulls. Typically this will be a type where the housing stop looks like this:

And the cable anchor looks like this:

It can be hard to make out in the photos, but the part that passes through the brake arm on each is a flatted oval type shape. It's the same on both so they can interchange. This is a standard of sorts that's been around a long time, such that generic replacement parts like the pictured ones exist and are common shop items.

Single pivot sidepulls are some of the weakest of all rim brakes. There are some double pivot calipers that can have their position switched in the same way. You're basically looking for ones that have the kind of housing stop and cable anchor pictured. There are some in Dia-Compe's line. I think this could be a good place to look. Be careful that whatever you get has a pivot bolt that matches the needs of the frame. Specifically, this bike likely can't take a recessed nut brake, and some of what you'll find is recessed nut only, but you may be able to circumvent that by using a front in the rear or switching pivot bolts.

Upside-down routing always has the disadvantage of the housing being open to the elements in a way where gravity is working in favor of water/dirt ingress. There are various nosed ferrule and boot type products that have attempted to address this - see Brompton brakes for an example. Another approach is to just switch the routing to continuous, zip tie it up the seat tube and then back down, and use one of the various fancy compressionless housing options that will take the extra bends without adding a lot of friction. Then you could use whatever dual pivot brake you want of the appropriate reach and mounting type, which is likely the path to getting the most power you can in the application.