It is possible to do SGAP after lat flap and doesn't really change the way the operation is done done overall.
The SGAP is a specialized procedure that requires far more expertise and experience than the tummy operations we do to get a result that is likely to perform properly. I don't know of anyone in your area that routinely performs double SGAP in same operation. We do them routinely to the extent that 6 were completed in our facility this week. Be sure you have a well experienced team and don't be afraid to ask, you've been thru a lot and I recommend you make no compromises that are avoidable.