Photoshop and Illustrator function completely differently; not only are they designed to work on different kinds of artwork, they have to "think" differently to do what they do. That means that very few of the COMPONENTS of the artwork they create and edit are directly compatible with each other. This fact makes it difficult to move artwork back and forth to edit it.
That said, Adobe understands that you may want to try, so they give you the option to export. With "maximum editability". I downloaded your file and tried it myself.
First, you didn't embed an image, so I just deleted that layer to continue my testing.
Second, I tried File > Export...; "Photoshop (*.PSD)" check "Use Artboard" select "All" > Export; color model "RGB" resolution "High (300ppi)" options "Write Layers" selected "Maximum Editability" checked > OK. A notification comes up and says "Some containers in the AI document have been flattened." When I open that document, it is indeed completely flattened.
Next, I ungrouped EVERYTHING (that is a chore, the blends need to be done manually) and tried again (same settings); there was no warning and there were some editable layers in the PSD.
So, tweak your artwork, ungroup and export. Repeat until you get the results you want in Photoshop.