The only conductors, besides the factory installed conductors, allowed in the meter side are the SE conductors.
The only legal ways to use the genny on this install is to....
1). Feed the ATS off the load side of one of the breakers to only one of the panels
2). Get two ATS, feed one ATS from the 200A breaker and feed the other from the 125A breaker, then feed a panel from each ATS respectively.
3). Run desired circuits to be backed up from both panels into a single panel and feed it from the ATS, feed the ATS from the 200A breaker.
This would be the most costly and hard to do choice. IMO.