What LCD TV do you have anyways? Does it say it can support 1080p for sure? There's a hack that can raise the bar on native resolutions as long as you're using DVI. I did this sa XRIGS(USC-TC) and managed to get 1600x1200 with the hack. I'll post the hack as soon as I find it. It's a really simple hack BTW.
EDIT: Here,

Use a dvi-vga dongle so you wont screw your beautiful monitor. See those two red pins? Take them off using a cutter.
WARNING: I am not responsible for any damages this hack may cause. But I as having tested it myself, it indeed works.