How to get pure black shadow on gradient shader

I need some help with a gradient shader. The code is posted below and it should render the material as a gradient based on the screenspace y position. There's two issues with this code. One, it's probably best to shift it to a vertex (or frag?) calculation instead of doing it all in surface. Second, I want to add a custom lighting model so that all shadows would be pitch-black instead of a darkened shade.

Shader "Custom/shdGrad1" {

 Properties {
 
   _ColorLow ("Color Low", COLOR) = (1,1,1,1)
   _ColorHigh ("Color High", COLOR) = (1,1,1,1)
   _yPosLow ("Y Pos Low", Float) = 0
   _yPosHigh ("Y Pos High", Float) = 10
   _GradientStrength ("Gradient Strength", Float) = 1
   _EmissiveStrength ("Emissive Strengh ", Float) = 1
   _ColorX ("Color X", COLOR) = (1,1,1,1)
   _ColorY ("Color Y", COLOR) = (1,1,1,1)
 
 }
 
 SubShader {
     
     Tags { 
         
         "Queue" = "Geometry"
         "RenderType" = "Opaque" 
         
     }
     
     CGPROGRAM
     #pragma surface surf Lambert addshadow
     #define WHITE3 fixed3(1,1,1)
     #define UP float3(0,0,1)
     #define RIGHT float3(1,0,0)

     fixed4 _ColorLow;
     fixed4 _ColorHigh;
     half _yPosLow;
     half _yPosHigh;
     half _GradientStrength;
     half _EmissiveStrength;
   
     struct Input {
         
         float2 uv_MainTex;
         float3 screenPos;
         float3 normal;
         
     };
     
     half3 gradient;
     half3 finalColor;
     
     void surf (Input IN, inout SurfaceOutput o) {
         
         // gradient color at this height
         gradient = lerp(_ColorLow, _ColorHigh,  smoothstep( _yPosLow, _yPosHigh, IN.screenPos.y )).rgb;
         
         // lerp the 
         gradient = lerp(WHITE3, gradient, _GradientStrength);
         
         // add the gradient color
         finalColor = gradient;            
             
         // scale down to 0-1 values
         //finalColor = saturate(finalColor);
      
         // how much should go to emissive
         o.Emission = lerp(half3(0,0,0), finalColor, _EmissiveStrength);
      
         // the "color" before lighting is applied
         o.Albedo = finalColor * saturate(1 - _EmissiveStrength);
      
         // opaque
         o.Alpha = 1;
         
     }
     
     ENDCG
     
 } 
 

fallback "VertexLit"

}

Any advice?

Many thanks to Reddit user CatchCo for the original code.