The transmission that is in your vehicle is a RE4FO4B, the problem your explaining sounds like the transmission is flaring. If when driving it feels like the vehicle goes into neutral their is a pressure issue inside. It may be as simple as a bad EPC solenoid, which is the electric pressure control, that would have to be checked via a scan tool with data flow and looked at by someone who is qualified to decipher the readings. I would have to think though that it is going to be an internal pressure loss, which means that one of the seals internally is not holding pressure. If this is the case there is no way around rebuilding or replacing the transmission.
Snotrans is absolutely right. The tranny is shifted by a command from the computer. This will only happen if the computer receives the correct signal from the vehicle speed sensor. If the tranny worked fine before the engine swap, then an unplugged sensor, broken wire or connector, or possible blown fuse are the most likely causes. Always verify fluid level and condition also. Burnt smelling fluid indicates a slipping clutch. A good transmission shop can scan the car and find the issue.