Dithering Transparency of opaque object, dithering received shadow and rendering shadows "behind" it

I have a dithering transparency shader that will make a screen-door effect on an opaque object.
The reason is that I want to create a fading cealing when the player enters a building.
However, the shader will not allow shadows behind the object to be rendered (picture attached). Besides that, I'd like to dither the "received shadows" on the object aswell.
What solution do you think would be most appropriate for this?

I'm using Unity 2018.4.14f1 standard 3D.



The shader:

Code (CSharp):

1. Shader "TEST/Dithering (Simple)"
2. {
3.     Properties
4.     {
5.         _MainTex ("Base (RGB)", 2D) = "white" {}
6.         _Transparency ("Transparency", Range(0,1)) = 1.0
7.     }
8.  
9.     SubShader
10.     {
11.         Tags
12.         {
13.             "RenderType"="Opaque"
14.         }
15.  
16.         CGPROGRAM
17.         #pragma surface surf Lambert noforwardadd
18.  
19.         sampler2D _MainTex;
20.  
21.         struct Input
22.         {
23.             float2 uv_MainTex;
24.             float4 screenPos;
25.         };
26.  
27.         half _Transparency;
28.  
29.         void surf (Input IN, inout SurfaceOutput o)
30.         {
31.             fixed4 c = tex2D(_MainTex, IN.uv_MainTex);
32.             o.Albedo = c.rgb;
33.             o.Alpha = c.a;
34.             // Screen-door transparency: Discard pixel if below threshold.
35.             float4x4 thresholdMatrix =
36.             {  1.0 / 17.0,  9.0 / 17.0,  3.0 / 17.0, 11.0 / 17.0,
37.             13.0 / 17.0,  5.0 / 17.0, 15.0 / 17.0,  7.0 / 17.0,
38.             4.0 / 17.0, 12.0 / 17.0,  2.0 / 17.0, 10.0 / 17.0,
39.             16.0 / 17.0,  8.0 / 17.0, 14.0 / 17.0,  6.0 / 17.0
40.             };
41.             float2 pos = IN.screenPos.xy / IN.screenPos.w;
42.             pos *= _ScreenParams.xy; // pixel position
43.             clip(_Transparency - thresholdMatrix[pos.x % 4] [pos.y % 4]);
44.         }
45.         ENDCG
46.     }
47.     Fallback "VertexLit"
48. }

This is the effect I'm looking for without Shader Graph:
- Dithering Transparency
- Dithering received shadow
- Rendering shadows behind the object