I've had luck occur in the negative direction concerning uverse.
As far repeating to combat a relatively small range with the wireless router they sent you:
Repeating shouldn't be a problem. Just get the hardware to wirelessly repeat. You automatically cut the (local) bandwidth maximum in half by doing this, so keep that in mind, especially if they sent you a 'G' router in late 2011, with 'N' hardware being available for at LEAST half a decade (they probably did).
If you can maintain a 54 Mbit connection, that leaves you with 27 Mbits if you connect via one repeater. Since your internet connection is probably in the 3-12 Mbit range, this shouldn't be a problem, assuming you can keep a relatively strong connection between the routers themselves, and the your access point router to your device.
You can also just turn off the wireless functionality of the router/modem they gave you, and just use it as a modem. Get a separate decent N router for like $20, and start with that. If you still need to repeat that, you'll have a lot more wiggle room. You might also look for a router which supports WDS out of the box, and just buy 2 or 3 of those to handle covering your area.