The CPU in the NAS isnt powerful enough to transcode media in real time as you found out.
Best plan of attack, sticking with the Synology you might get away with audio transcoding on the Synology and Yamaha, there should be some basic audio transcoding settings in the media server settings. If thats no good purchase TVMobili
and install that on the Synology, it has built in transcoding or try Serviio which is free but requires the annoying java to be installed on the NAS.
The CPU is usless for transcoding video so return or sell the Sony and get a media player with better media support to replace it, for example Samsung, Toshiba, LG all have far superior media players compared to Sony BD players.
* Return the Synology, next generation Intel CE5300 based NAS with hardware transcoding support are just around the corner from the likes of Thecus (N2520 series), Synology and Asustor (AS3 series) . This should give you the real time transcoder that you need though these NAS will be more expensive.
* Convert everything into a format supported by both devices.