For what I know, Lapsed IR is not a problem ,I did my TR with IR lapsed,When you do your TR ,Your IR will be renewed in the type of aircraft you fly.
They are no formalities to be carried out in DGCA , I went directly , making sure that the trto is ICAO approved, which almost every TRTO is.
There is a syllabus on DGCA website which has to be strictly followed ,
Earlier they used to ask us to get a NOC , but now it's not required , you can read the legislation laid down in the DGCA CARs
The choice of trto is strictly yours , the two you have mentioned are icao approved and apart from the two you have mentioned , almost every one adheres To industry and icao standards.