Problems with BlendOp Max

I'm trying to write a shader that doesn't blend additively etc etc. I'd like to take whichever of the source or destination colours is brighter and use that and BlendOp Max seemed like the tool for the job.

However, as you can see below, the shadow of one light seems to be occluding the other, which doesn't match up with how I understand BlendOp Max is supposed to work:

• Unity Docs
• NVidia
• OpenGL

Could anyone clarify where I'm going wrong or provide an alternative?

Interestingly, Blend One One is working fine, however, BlendOp Add (along with all the other BlendOps apart from the 'logical' ones) are creating the same issue.

Update

Shader Code:

Shader "Lantern/Flat Pullup" {
Properties {
    _LitTex ("Lit (RGB)", 2D) = "white" {}
    _UnlitTex ("Unlit (RGB)", 2D) = "white" {}
    _Pullup ("Pull up Point", Range(0,1)) = 0.7
    _BlendSize ("Blend Size", Float) = 0.3
}
SubShader {
    Pass{
        Tags { "LightMode" = "ForwardBase" }
        LOD 200

        CGPROGRAM
        #pragma vertex vert
        #pragma fragment frag
        #include "UnityCG.cginc"

        uniform sampler2D _UnlitTex;
        uniform float4 _UnlitTex_ST;
        uniform sampler2D _LitTex;
        uniform float4 _LitTex_ST;
        uniform float _Pullup;
        uniform float _BlendSize;

        uniform float4 _LightColor0;

        struct VI {
            float4 vertex : POSITION;
            float4 tex : TEXCOORD0;
        };

        struct V2F {
            float4 pos : SV_POSITION;
            float4 tex : TEXCOORD0;
            float4 posWorld : TEXCOORD1;
        };

        V2F vert(VI v){
            V2F o;
            o.pos = mul(UNITY_MATRIX_MVP, v.vertex);
            o.tex = v.tex;
            o.posWorld = mul(_Object2World, v.vertex);
            return o;
        }

        float4 frag(V2F i) : COLOR {
            float3 flatReflection = _LightColor0.xyz * 
                (1 / length(_WorldSpaceLightPos0.xyz - i.posWorld.xyz));

            return lerp(
                tex2D(_UnlitTex, i.tex.xy * _UnlitTex_ST.xy + _UnlitTex_ST.zw),
                tex2D(_LitTex, i.tex.xy * _LitTex_ST.xy + _LitTex_ST.zw),
                clamp((length(flatReflection) - _Pullup + _BlendSize) / (2 * _BlendSize), 0, 1)
            );

        }

        ENDCG
    }

    Pass{
        Tags{"LightMode" = "ForwardAdd"}
        //Blend One One
        BlendOp Max
        LOD 200
        CGPROGRAM
        #pragma vertex vert
        #pragma fragment frag
        #include "UnityCG.cginc"

        uniform sampler2D _UnlitTex;
        uniform float4 _UnlitTex_ST;
        uniform sampler2D _LitTex;
        uniform float4 _LitTex_ST;
        uniform float _Pullup;
        uniform float _BlendSize;

        uniform float4 _LightColor0;

        struct VI {
            float4 vertex : POSITION;
            float4 tex : TEXCOORD0;
        };

        struct V2F {
            float4 pos : SV_POSITION;
            float4 tex : TEXCOORD0;
            float4 posWorld : TEXCOORD1;
        };

        V2F vert(VI v){
            V2F o;
            o.pos = mul(UNITY_MATRIX_MVP, v.vertex);
            o.tex = v.tex;
            o.posWorld = mul(_Object2World, v.vertex);
            return o;
        }

        float4 frag(V2F i) : COLOR {
            float3 flatReflection = _LightColor0.xyz * 
                (1 / length(_WorldSpaceLightPos0.xyz - i.posWorld.xyz));
            return lerp(
                float4(0,0,0,1),
                tex2D(_LitTex, i.tex.xy * _LitTex_ST.xy + _LitTex_ST.zw),
                clamp((length(flatReflection) - _Pullup + _BlendSize) / (2 * _BlendSize), 0, 1)
            );
        }
        ENDCG

    }
}   
FallBack "Diffuse"
}

Update 2

The same plane and lights rendered using Unity's standard shader, for illustrative purposes.