How can I calculate the worst-case Tj of a MOSFET in discontinuous operation at another Tamb?
I suggest measuring the characteristics of the parts you have (rdson, etc) and then measure the temperature. Compare this with your calculations to gain confidence in your model.
Then you can recalculate temperature based on worst case component characteristics.
Also note that Rdson is based on junction temperature, and not only ambient.
Also, 1 minute seems a long time. I would design for steady-state.