1st thing I would suggest is open and clean all of the electrical connections and switches. DeOxit electrical contact cleaner will be your friend.
Ignition switch, Kill switch, ECU multipin connector, the main frame ground point under the fuel tank, the ground wire connection at the starter, any intermediate connectors, plug in relays, air temp sensor, water temp sensor,...... you get the idea, as much as you can access.
Pull the starter and check the brushes and carbon buildup.
As far as a replacement ECU, the fich part #'s are the same for the RS as the LT, so long as the type is the same. Meaning with or with out Catalytic converter. Still doesn't mean that the internal program is the same, just that they use the same programmable base control module.
Inge may know more about that......