Gaps between shapes when exporting from illustrator to photoshop

I often have .ai files that need to be exported to .psd but with paths retained. To retain all vectors I follow this tutorial. All works as fine, expect for the fact that I often end up having small hairline gaps between different shapes, the same shapes stick perfectly to each other in Illustrator or even an exported PNG.

Here's what it looks like as a PNG / AI

And this is what I get in Photoshop

Here's a few questions I came across on SE

Space between 2 paths in Illustrator

Fix gap between path and shapes in Illustrator

Hairline gaps between shapes

There are a few more that I went through, but can't find them now. In any case, they all had the same explanation and solution suggested.

1. 
   

   This is caused due to issues with Anti-Aliasing in Illustrator

   
   


2. 
   

   Solution 1 : Keep an object behind the area where the line shows up and give this object a favourable solid fill color

   
   
   


3. 
   

   Solution 2 : Use Illustrator's path offset feature to "grow" all shapes my a small unnoticeable amount so the shapes then appear to be contact

   
   

I can't use the first solution as these AI files are normally icons with no specific background, would be tedious to fill the gaps manually

The second solution is helpful, but more of something I would try if all else fails. This is because :

1. 
   

   The solution I followed to retain vectors needs all shapes to be converted to compound shapes before exporting. However, because of this, I tend to have a lot of compound shapes for each separate element. To make things worse, any group in AI get's exported as a rasterized layer. So I need to keep a rather long list of compound shapes.

   
   
   


2. 
   

   When using the offset feature, I noticed that it adds a slightly larger new path below the selected shape, which means I'll have even more elements to handle now. This doesn't seem like a problem with simple designs, however when it comes to larger complex artworks things get quite messy.

   
   

Are there any other ways of solving this problem.

EDIT :

Here's the AI file