If the Express's LED is flashing yellow, slowly, that indicates it's ready for you to configure it using AirPort Utility. If it isn't, perform another "hard reset".
You need to specifically join its network by selecting it in your Mac's Wi-Fi menu. Depending on your OS X version, it will either appear as "New AirPort Express..." (recent OS X versions) or "Apple Network nnnnnn" (earlier OS X versions). That is a temporary open network it creates for the purposes of configuration. Select it, and then use AirPort Utility.
During that time you will no longer have an Internet connection, because your Mac will be connected only to the Express.
After you configure it and resolve any configuration errors that may result, click Update. As the Express restarts, the temporary open network it created will cease to exist, and AirPort Utility is likely to report "An unexpected error has occurred". The reason that happens is that the Express is no longer creating a network in Client Mode and will no longer appear in AirPort Utility. At that point, just quit AirPort Utility and re-join your existing wireless network by selecting it in your Mac's Wi-Fi menu. The temporary Express network may remain visible in that menu for a while, but it will eventually disappear.
The Express's LED should illuminate solid green, and its speakers should then appear as an output option in apps that support AirPlay streaming such as iTunes.
As you might imagine using a non-Apple router complicates things a bit, and since I don't use one of them I am unable to provide more specific instructions. What you propose is certainly achievable though. Let me know if you still get stuck.