As suggested by hv, I got the $^N working. Again you need to know the nesting in advance. This is the $2 & $3 bit:

(?= (??{ qr!.{$a[2][0]}! }) 
   ( # start $2
      (?= (??{ qr!.{${\($a[3][0]-$a[2][0])}}! })                      
+                  
          ((??{ qr!.{$a[3][1]}! })) ) # $3 nested
      (??{ qr!.{$a[2][1]}! })
   ) # $2 ended
)
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