Hope this statement is okay to you.
The rotor terminals are shorted here; no significant change in torque characteristic
Not of the SRIM - but it won't make them the same as an equivalent SCIM.
The motor of the OP appears to be his Hobson's choice; The efficiency does not seem to matter to him.
He has a choice. Keep the existing SRIM or change it to a SCIM.
I know it's somewhat off topic but a few words about the control of SRIM machines.
Rated voltage and frequency is applied to the stator and control is on the rotor side.
The rotor voltage and frequency are maximum at standstill and close to zero at maximum speed.
For a centrifugal load, the maximum controlled power is about 15% and converter losses are proportional to that in contrast with a variable frequency inverter where the controlled power is 100% of rated power with losses accordingly.
On one project where we offered both the difference in efficiency, including the motor, was about 3% at top speed and around 5% at minimum speed. That may not sound like a lot but that difference amounted to enough to pay back capital cost in about three years. Efficiency matters. Seriously matters.
A couple of other points for you and others to see where I'm coming from.
If you just deal with 15% in conversion you have a similar reduction in harmonics.
And the motor can be connected directly to the incoming supply. The motor on the project to which I referred was an 11kV machine. The customer incoming supply is 11kV so no need for a transformer to reduce the supply to drive input voltage.
The VSD option, 690V, would have required a step down transformer with additional attendant losses.
I'm not suggesting that approach here. It is application specific.
The correct route, in my opinion, is to replace the motor with a SCIM unit.