Q: Connecting an Airport Express to my multiroom home audio system

I am interested in streaming music from my ipad (locally on my ipad as well as itunes) so I can enjoy listening to it through my wired home audio system.  I have a Russound system with wired speakers in 6 rooms of my home.  Each room has a keypad which controls inputs from 6 different sources.  My sound system installer gave me the idea of purchasing an Airport Express as a way to listen to my music since it has an audio ouput.  My installer is excellent at hooking up home audio equipment and working with the Russound equipment, but networking is not one of his strengths.

My current network setup is as follows.  All of my home audio equipment, cable modem, main router and network switch is located in a basement network closet.  I have a cable modem connected by ethernet to a linksys wireless n-router.  This router is then connected to a 32 port switch.  From the 32 port switch, I have multiple ethernet Cat5e cables going to various outlets throughout my home.  I also have a multiple extra cables ran into my attic space for future use.  My home is sprawling so the linksys wireless n-router will not come close to reaching every room.  I have another linksys wireless n-router plugged into one of the ethernet jacks on the other end of the house to use as an access point.  So basically my whole home has wireless coverage (via the two linksys routers)and wired coverage via multiple ethernet jacks throughout my home.

My plan was to use the Airport Express in bridge mode and put it in the basement network closet where my network switch and home audio equipment is located.  From just plugging in the Airport Express without setting it up, it doesn't seem to have enough wifi signal strength to come close to reaching all parts of my home (which I expected).  My ipad is going to have problems picking up the signal via Airplay in order for me to use it in several of the rooms on the other side of the house.  I need a way to get wireless signal from the Airport Express in the basement network closet to the other end of my home.

I thought the best solution would be to add a second Airport Express (or possibly a third Airport Express if necessary) to get signal that my ipad can see on the other side of my home.  Can these be hooked up to the Airport Express in the basement network closest by my ethernet network?  I don't need to connect them wirelessly as I have plenty of ethernet jacks hardwired throughout my home.  And if so, will I be able to connect my ipad to either the second Airport Express (or third Airport Express if necessary) that I add and still be able to listen to music even though these Express units do not have a direct connection to my home audio system?  I am basically looking at a way to extend the wifi signal from the basement closet Airport Express to use Airplay on my ipad at a distance where I have little to no signal.

I would greatly appreciate any thoughts.  Thanks!