Moving outside shower drain from dry well to storm drain

[Offguard-2]

I have an outside shower that drains to a dry well. It doesn't last long (maybe 1 to 2 minutes) before the water starts to come back up the drain. My neighbors have there outside shower drains connected to the storm drain that lets out on the street. I'd like to connect my shower drain to the storm drain, which runs right by the shower and the dry well.

Initially, I thought I could connect to the storm drain along the shower drain drop. My concern with this approach is that:
1) the shower drain drops 21" before turning 90 degrees towards the dry well
2) the drain sits in a concrete slab (about 6" thick).
3) the storm drain doesn't seem that deep so I don't know how I'd get the drop necessary

I'm hoping to avoid breaking any concrete, which is why I wanted to share and idea and get feedback.

I was hoping to use the punch out in the Flow Well as the connection point and push the shower water to the storm drain (about 2 feet away). Would this be possible? My assumption that when it fills towards the top that the water would run to the the outlet pipe.

Encouraged to hear why it would or would not work from plumbing experts.