Do a Google search on Manchester encoding before you go any farther.

I'm using the same modules you are using and they work great for me, both TX'ing and RX'ing at 9600 baud over 200-300 feet at 5v on the TX and RX using roughly 11 inch wire antennas.

Send about 5ms worth of 1's and 0's before you do anything with the transmitted data...a $55AA will do to sync up the data slicer on the RX, more if you can spare the time. Then immediately after that send your data.
This should be manchester encoded, which also happens to double your data payload...2400 baud becomes 1200 baud of actual data sent. 0's become '01' and 1's become '10'. I just use a lookup table to do both the encoding and decoding conversion...simple enough and avoids any complex logic at both ends. And don't wait between characters. With those modules, the data slicer begins to discharge itself after a couple of milliseconds. If you pause the data stream, the data slicer will lose it's mind and you'll have to send more sync-bytes. Check out www.laipac.com for a bit more in-depth information on those type modules.

More advise from me that may work for you (or not, who knows), switch over to 4800 baud, maybe 9600 if it ends up working (I've had 19,200 baud working intermittently at 200 feet). With the 4800 or 9600 baud rate, you can send more sync-bytes ($55AA) to help set up the receiver.

JDG