There are many variables that affect brake performance. But let's deal with the simplest to assess-- leverage.

Despite advert claims the leverage issue is really simple. You have roughly 2" of lever travel, and need a few millimeters of shoe travel. Those are inherent properties of all rim brakes, with little room to maneuver. If you want to increase the rim/shoe clearance, you have to lower the leverage or get bigger hands. If you want more leverage, you need to accept less shoe clearance.

Now the leverage is determined in two steps, within the caliper and within the lever. Different brakes have different leverage in the calipers, and the makers compensate with levers that restore the total leverage ratio to the target range. That means that mixing levers and calipers can change the leverage ratio, causing high leverage brakes that barely open, or brakes that call for excess lever travel.

You're excess lever travel could be from poor (too open) adjustment, but if the shoes barely open, and you have excess lever travel, then it sounds like a parts mismatch.

There are other factors, such as flex or sloppiness in the caliper (it's rare in the lever), poor shoe selection, excess toe-in, etc. but start by confirming that roughly 1" of travel is enough to move the shoes 4mm or so leaving 2mm open clearance.