Does the manual *say* it can do 1360x768 over VGA or does it just say the native panel resolution is 1360x768. Those are 2 different things.
My only experience is with Sony Bravia KLV-S32A10. What I found was that even though the native panel res was 1360x768, there were 2 problems with displaying that video format.
1) 1360x768 is missing from the panel's EDID info
I was surprised to see this, but when I looked in the manual, in fact it said 1280x768 was the highest resolutio it supported over VGA. After some fiddling I was eventually able to get 1360x768 to sync correctly, which leads to the next problem
2) at 1360x768 there is vertical banding in the picture. No matter how you adjust phase/pitch in the WEGA gate controls, you can not get rid of the banding. The banding is caused by the pixels not mapping consistently from the video signal to the panels pixels. Sometimes they line up, sometimes what is in the video signal is split among 2 panel pixels. I tried a ATI R9800 Pro and PNY Verto 6600GT with same results, so I assume the issue is on the panel side.
People tell me the XBR models don't have these issues, but I haven't tested that out myself.