How to convert this shader from Worldspace into Localspace?

Question

Based on this question (LINK)

Shader "Unlit/WorldspaceTiling"
{
    Properties
    {
        _MainTex ("Texture", 2D) = "white" {}
    }
    SubShader
    {
        Tags { "RenderType"="Opaque" }
        LOD 100

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

            struct appdata
            {
                float4 vertex : POSITION;
                float2 uv : TEXCOORD0;
            };

            struct v2f
            {
                float2 uv : TEXCOORD0;
                float4 vertex : SV_POSITION;
            };

            sampler2D _MainTex;
            float4 _MainTex_ST;

            v2f vert (appdata v)
            {
                v2f o;
                o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);

                // Gets the xy position of the vertex in worldspace.
                float2 worldXY = mul(_Object2World, v.vertex).xy;
                // Use the worldspace coords instead of the mesh's UVs.
                o.uv = TRANSFORM_TEX(worldXY, _MainTex);

                return o;
            }

            fixed4 frag (v2f i) : SV_Target
            {                   
                fixed4 col = tex2D(_MainTex, i.uv);
                return col;
            }
            ENDCG
        }
    }
}

So this has these two issues:

• a) If the object moves through worldspace (eg. a moving platform), the texture will appear to crawl along it.
• b) Rotating the object won't rotate the texture, so it will tile across it diagonally.

How is this code supposed to be to fix these two problems?

EDIT:

This is what I'm trying to achieve over all:

I have no idea if my current method is good or bad, but its basically:

1. Use a flat mesh created in blender with UVs unwrapped. They're all basically a bunch of quads with UVs having literally the shape same as the mesh itself.
2. Attach a material to each mesh in Unity with a particular texture.
3. Resize, rotate and align mesh into correct size and position.
4. Use as physics object in a 2D sideview game. May have additional meshes attached to it as non-interactive decorations, but otherwise using the same method to build them.