It appears that this is not possible using the RTF Writer Library. It seems to have no support for loading, parsing or merging other RTF data.
For what it's worth, my requirements have changed so I no longer need to do this. However, I was on the verge of making my own RTF parser and merging tool. Merging RTF is not as simple as copy/paste due to the way that the RTF format handles styles. Styles such as fonts and colours are defined in header tables which makes the merging more complicated.
Anyone wanting to try something for themselves may find some useful information: Here, here and here.