No, taking Bharatpur-Sawai Madhopur-Jaipur route is impossible.
The total distance will be 315 km. As per TT, BTE-JP is allocated 3:07 hours and you said train arrived 1 hour BT. Therefore according to your theory, the train covered 315 km in 2 hours, which is 157 km/h. I don't think this train can run faster than Vande Bharat Express. So it's obvious that train is running via Bandikui only.