The LA1034 is now connected to the MIC plug. The communication protocol seems to be SPI, at least that how I'm decoding it with the "Synchronous Serial" interpreter.
The frequency can be easily identified but there are still lots of things to discover:
09/19/2012: One more evening spent playing with the RC-10. I've found how to set the TM-241E to correctly send the frequency to the RC-10, but it disables all other informations in the data frame. At least I know my RC-10 is not faulty, the TM-241E seemed to use the RC-20 protocol to send the data out, which caused the erroneous frequency on the RC-10's LCD.
Now that I have almost all data frames I think I can start to write the protocol specifications. I've also found hidden functions on the RC-10. I'll post all that stuff in a PDF ASAP.
09/21/2012: I've finally had some time to write some description of the protocol. This is still a draft though. Protocol Specifications