That means something is deforming or compressing as you squeeze harder.

If you really just want the lever not to hit the handlebar, take out as much free cable and reduce the tire clearance as your wheels can stand. It won't make the lever less spongy but it will give you more lever movement capacity.

Sponginess can come from several sources. Long cable runs always feel worse than short front ones. Housing ends that don't fit well into whatever stops you have can be a source. Make sure the pads hit the rim square on so that they don't deform after they first contact the rim. Make sure the cantilever pivots are solid. Anything that gives the lever higher mechanical advantage at the caliper also produces more stress in the components and more tension in the cables, which could mean more deformation or stretching. For that reason, shorter straddle cable could actually make it feel worse if you don't need that much mechanical advantage to get sufficient braking.