$1000 is a decent starting point, I would agree with rojo and do not see the need for towers, but see a need to upgrade judging by your current list...
I would start with a strong sub, I am not sure on your room dimensions but the sub is going to give you the most satisfaction for your money...
VTF2 by HSU research would be nice, they are on sale rite now, I own 2 of them and even with just a single lit, it over powers my -400sq foot room and 200w per channel mains...
VTF-2 MK4 Subwoofer
So there goes 1/2 of your budget, lol..
Now onto your front sound stage, your front left, right, and center... there are a lot of options out there for bookshelfs, lower budget stuff like the wave crest {$335 for 3 of them}
HVL-1 Two-Way Loudspeaker | Wave Crest Audio, the pioneer andrew jones center and books, ascend 200's, ect are all decent but I like the output and sq from the wave crests, they are nice for the money...
Now for your surrounds {stay with 5.1}, I would leave the rsx3's back there and if you ever upgrade your fronts move the wave crests back there....
As for your avr, if you want to upgrade that also and stretch your budget, this seems like a good deal
DENON AVR-E300 5.1 3D Networking Receiver AirPlay | Accessories4less..
I have heard the wave crests {5 of them} with an HSU vtf2 and a decent entry level avr {pioneer 1122} in a 325sq ft room and the setup really sounds like something that cost much much more. The vtf2 is low, hits hard, and has very strong clean output the wavecrests are clean, clear, and don't seem like they need a ton of power to get loud {bookshelfs tend to need more wattage to make a lot of sound}...
There are a lot of sales and decent deals around, do some in home testing {most companies will ship to you and take returns if you are not happy}, and for heavens sake hard wire your surrounds!!!