Shader Transparency issues

I've slightly modified this shader (video) (git repo) to achieve echolocation in my game. I've gotten it to work really well, but the only issue is it lacks transparency.

The shader functions like this (excluding the distortion - that's handled separately and has no effect on the shader)

I've tried following this answer to add transparency to the shader, but the results are not what I'm looking for.

Here's an image describing my issue:

This shader uses a distance variable to control how the echolocation rendering moves outward from the player. How can I fix these issues? Any and all help is appreciated! I'm pretty clueless when it comes to shaders, but I really need transparency in my game.

Here's a diff between the two shader versions below to save you some time. Here's my non-transparent shader code:

  Shader "My/Normal/AlphaPulseShader" {
      Properties{
          _MainTex ("Base (RGB) Trans (A)", 2D) = "blue" {}
          _BumpMap ("Normalmap", 2D) = "bump" {}
          _EmissionMap ("Emission Map", 2D) = "black" {}
          _Color ("Color", Color) = (1,0,0,1)
          _PDistance ("PulseDistance", Float) = 0
          _PFadeDistance ("FadeDistance", Float) = 10
          _PEdgeSoftness ("EdgeSoftness", Float) = 5
          _Origin ("PulseOrigin", Vector) = (0, 0, 0, 0)
  
          _RimColor ("Rim Color", Color) = (1,1,1,1)
          _RimPower ("Rim Power", Range(0.5, 8.0)) = 1.059702
          [Toggle(USE_RIM)]_RimOn ("Rim On", Int) = 0.0
          _EmissionMultiplier ("Emission Multiplier", Range(-10,10)) = 1.0
      }
  
      SubShader{
          Tags{ "RenderType"="Opaque" }
          LOD 200
  
          CGPROGRAM
          //LIGHTING
          #include "AutoLight.cginc"
          // define finalcolor and vertex programs:
          #pragma surface surf Lambert finalcolor:mycolor// alpha
  
          #pragma shader_feature USE_RIM
  
          struct Input {
              float2 uv_MainTex;
              float2 uv_BumpMap;
              float2 uv_EmissionMap;
              float3 worldPos;
              float3 viewDir;
              half alpha;
          };
  
          fixed4 _Color;
          sampler2D _MainTex;
          sampler2D _BumpMap;
          sampler2D _EmissionMap;
          half _PDistance;
          half _PFadeDistance;
          half _PEdgeSoftness;
          float4 _Origin;
  
          float4 _RimColor;
          float _RimPower;
          float _RimOn;
          float _EmissionMultiplier;
  
          void mycolor (Input IN, SurfaceOutput o, inout fixed4 color) {
              // set the vertex color alpha to the value calculated: 
              fixed4 c = tex2D (_MainTex, IN.uv_MainTex) * _Color;
              color.a = c.a;
              half dis;
              half interval;
              half origin;
              dis = sqrt (pow ((IN.worldPos.x - _Origin.x),2) + pow ((IN.worldPos.y - _Origin.y), 2) + pow ((IN.worldPos.z - _Origin.z), 2));
  
              if (dis >= _PDistance)
              {
                  color.rgb = color.rgb * (1 - saturate (abs (_PDistance - dis) / _PEdgeSoftness));
              }
              else
              {
                  color.rgb = color.rgb * (1 - saturate (abs (_PDistance - dis) / _PFadeDistance));
              }
  
          }
  
          void surf (Input IN, inout SurfaceOutput o) {
              // simply copy the corresponding texture element color:
              fixed4 c = tex2D (_MainTex, IN.uv_MainTex) * _Color;
              o.Albedo = c.rgb;
              // o.Alpha = tex2D(_MainTex,IN.uv_MainTex).a;
              o.Normal = UnpackNormal (tex2D (_BumpMap, IN.uv_BumpMap));
              //  half rim = 1.0 - saturate(dot(normalize(IN.viewDir), o.Normal));
              #ifdef USE_RIM
                  half rim = 1.0 - saturate (dot (normalize (IN.viewDir), o.Normal));
                  o.Emission = _RimColor.rgb * pow (rim, _RimPower) + _EmissionMultiplier * tex2D (_EmissionMap, IN.uv_EmissionMap);
              #else
 
                  o.Emission =  _EmissionMultiplier * tex2D (_EmissionMap, IN.uv_EmissionMap);
              #endif
          }
          ENDCG
      }
      // Fallback "Diffuse"
      Fallback "VertexLit"
  }

And here is my modified shader code for transparency:

  Shader "My/Normal/AlphaPulseShader" {
      Properties{
          _MainTex ("Color (RGB) Alpha (A)", 2D) = "white" {}
          _BumpMap ("Normalmap", 2D) = "bump" {}
          _EmissionMap ("Emission Map", 2D) = "black" {}
          _Color ("Color", Color) = (1,0,0,1)
          _PDistance ("PulseDistance", Float) = 0
          _PFadeDistance ("FadeDistance", Float) = 10
          _PEdgeSoftness ("EdgeSoftness", Float) = 5
          _Origin ("PulseOrigin", Vector) = (0, 0, 0, 0)
  
          _RimColor ("Rim Color", Color) = (1,1,1,1)
          _RimPower ("Rim Power", Range(0.5, 8.0)) = 1.059702
          [Toggle(USE_RIM)]_RimOn ("Rim On", Int) = 0.0
          _EmissionMultiplier ("Emission Multiplier", Range(-10,10)) = 1.0
      }
  
      SubShader{
          Tags{ "Queue"="Transparent" "RenderType"="Transparent" }
          LOD 200
  
          CGPROGRAM
          //LIGHTING
          #include "AutoLight.cginc"
          // define finalcolor and vertex programs:
          #pragma surface surf Lambert finalcolor:mycolor alpha //check this out
  
          #pragma shader_feature USE_RIM
  
          struct Input {
              float2 uv_MainTex;
              float2 uv_BumpMap;
              float2 uv_EmissionMap;
              float3 worldPos;
              float3 viewDir;
              half alpha;
          };
  
          fixed4 _Color;
          sampler2D _MainTex;
          sampler2D _BumpMap;
          sampler2D _EmissionMap;
          half _PDistance;
          half _PFadeDistance;
          half _PEdgeSoftness;
          float4 _Origin;
  
          float4 _RimColor;
          float _RimPower;
          float _RimOn;
          float _EmissionMultiplier;
  
          void mycolor (Input IN, SurfaceOutput o, inout fixed4 color) {
              // set the vertex color alpha to the value calculated: 
              fixed4 c = tex2D (_MainTex, IN.uv_MainTex) * _Color;
              color.a = c.a;
              half dis;
              half interval;
              half origin;
              dis = sqrt (pow ((IN.worldPos.x - _Origin.x),2) + pow ((IN.worldPos.y - _Origin.y), 2) + pow ((IN.worldPos.z - _Origin.z), 2));
  
              if (dis >= _PDistance)
              {
                  color.rgb = color.rgb * (1 - saturate (abs (_PDistance - dis) / _PEdgeSoftness));
              }
              else
              {
                  color.rgb = color.rgb * (1 - saturate (abs (_PDistance - dis) / _PFadeDistance));
              }
  
          }
  
          void surf (Input IN, inout SurfaceOutput o) {
              // simply copy the corresponding texture element color:
              fixed4 c = tex2D (_MainTex, IN.uv_MainTex) * _Color;
              o.Albedo = c.rgb;
               o.Alpha = tex2D(_MainTex,IN.uv_MainTex).a;
              o.Normal = UnpackNormal (tex2D (_BumpMap, IN.uv_BumpMap));
              //  half rim = 1.0 - saturate(dot(normalize(IN.viewDir), o.Normal));
              #ifdef USE_RIM
                  half rim = 1.0 - saturate (dot (normalize (IN.viewDir), o.Normal));
                  o.Emission = _RimColor.rgb * pow (rim, _RimPower) + _EmissionMultiplier * tex2D (_EmissionMap, IN.uv_EmissionMap);
              #else
 
                  o.Emission =  _EmissionMultiplier * tex2D (_EmissionMap, IN.uv_EmissionMap);
              #endif
          }
          ENDCG
      }
      // Fallback "Diffuse"
      Fallback "VertexLit"
  }