Electric Motor Design

I found another possible approach in:
https://www.femm.info/wiki/RapidIMAnalysis.

Summary:
1. replace squirrel cage rotor with equivalent 3ph winding
2. Analysis is carried out in synchronous dq-frame
3. Iterativeley determine rotor current. Start with i_dr = 0; i_qr = -iq_s
3. Calculate stator ...

The thing to consider is what you need the equivalent circuit for.
If you're after the "Steinmetz" T-type equivalent circuit, then the approach outlined in the OP is appropriate. Or simulate no-load / locked-rotor tests (which I believe is equivalent).

For an approached based on stored energy a lot ...