There are different side pull levers, but unless you are seeing a lot of flex in the calipers when you apply the brakes, it might not do a lot of good.

Unfortunately, I suspect that most modern brake pads are designed without any concern for good operation on steel rims. I often see recomendations for KoolStop Salmon pads... Those may be good for you.

If you are going to spend money to upgrade, I would sugest upgrading to alloy rims/wheels as you are addressing two issues (braking and weight) with one upgrade. And regardless of the pads, stwell rims are notoriously poor in wet conditions.

Also, since you should be doing most of your braking with the front wheel, you may be able to get along by only replacing the front wheel/rim.

I am assuming you have already checked things like cable condition etc... If your cables are meeting some resistance in the housing it could be robbing you of braking power as well.

To find a different set of brakes, be sure that you get single pivot, as I hear the modern caliper brakes mount differently from the vintage ones.

To be honest, if I were you and were to run into a bike with the right sized alloy wheels in a thrift store, I would upgrade the wheels and also try the brakes.