victa,
Are the transformer and motor new equipment? ie can you change the parameters? Where are your voltage drop limits?
The A/T can be tapped down to as low as 50%, however the torque will drop as the square of the voltage so the load torque needs to be low. What is the driven load and can it be started unloaded? The lower you can get the load torque during starting, the lower the voltage dip will be. Obviously a clutch or fluid coupling would be the best option but they present operational difficulties (maintenance, efficiency).
A VFD will get your motor away no matter what the load is - but again, the lower the starting torque the smaller and cheaper the VFD. You might 'only' need a 1500kW drive.
apowerengr's suggestion of a wound rotor is a good one and the resistance can be varied to get the inrush down to an acceptable level. Modern designs (eg WEG) have an elegant rotor shorting and brush lifting arrangement which means brush wear is very low.
Other alternatives that we have been involved with that might be worth a try: capacitors, capacitors and A/T together.