It will be virtually impossible to find a barrel extension that matches the one which split. The new barrel extension will have to be headspaced and pinned. Then the front sight base will have to be removed and a new gas port will have to be drilled. Lastly, the front sight base will have to be re-attached. It takes GO/NO GO gauges and precision fitting to do all that.
The bottom line is the "cheap route" will probably cost as much as buying a new complete barrel assembly.