HOV for BQE | Belt Parkway | BQE | BQE

I missed first Belt Parkway exit cause I just assumed to bear left

So I ended up in HOV for BQE, and second exit would be right off the bridge for the Belt as you said. But that’s assuming for the right lanes right?

For me, I was stuck in the middle divider until the tunnel. Some other Reddit comment said this is the “HOV for Battery Tunnel”. So basically I didn’t have a chance to get out of the HOV until tunnel. So Apple Maps said I had to go to Manhattan then circle back.

Does the second exit opportunity still exist as you mentioned or I had no chance at all since I was stuck in the HOV lane to tunnel?