The PLG150-DX is the board inside the DX200. They share the same patch formats at the board level. There is another level of editing above that, either DX200 or CS6x native which are NOT compatible.
The FS1R supposedly can load DX7 patches via sysex. The PLG150-DX can also do this from within the DX Simulator voice editor. The PLG boards cannot dump patches to anything other than a storage device of the host machine (Smart Media in the case of your CS6x) and this format can only be used to load the patches back into the board. The FS1R will not be able to read the files.
In other words you will not be able to do what you want to do.
I listened to Hatfield and the North at Rainbow. They were very wonderful and they made my heart a prisoner.