You could try manually opening up the ports that the UPnP/DLNA server uses (if it does use any as this is meant to happen automatically) through port forwarding however I couldn't tell you what they are, I had a look around and didn't see the info posted on the FAQ about ports
Maybe Synology tech support can tell you or if any Synology rep could step in and share the info.
I'd go with what Bosk suggested on the DD-WRT the click on router database and then copy/paste into the field WRT320N and it should show any compatible firmwares (download the mini generic firmware). Then flash the new firmware using the built in firmware flash in the Linksys web page config.
You should be able to flash back to original if its available to download from Linksys website or you can dump/backup with current Linksys firmware but I cant make any guarantees as I dont have that router. Of course flashing a custom firmware carries risks of bricking it etc you get the idea.
One thing you could do is borrow a friends router and see if a different brand router (not Linksys) makes a difference, if it all works then you know the router is the problem.