You need a T-45 from a '96, 97 or 98 GT for your '98 GT. The T-45 from a 96-98 Cobra could be made to fit, but the crossmember mount is farther back to clear different catalytic converters from the factory. Also, the cobra t-45 has a 7 tooth drive gear for the speedometer, the GT trans has an 8 tooth drive gear.
The TR3650 (mid 01-04) doesn't have the gear to drive the speedometer speed sensor. Also, the TR3650 has a 31 spline output shaft. I believe the T-45 has a 28 spline output.