Is there any way to make the iPad 2 mirror at 720p instead of 1080p?

My Westinghouse TV, which is 780p/1080i can't mirror the iPad 2 with the HDMI adapter, but my Vizio 1080p TV can. I get no signal on the Westinghouse, and the connection seems to reset every few seconds (almost constantly scanning for input). The product page for the adapter said "up to 1080p"- is this actually a hard requirement in iOS 6.0.1? Is there any way to set the mirror/export resolution on the iPad 2? I cannot change the resolution on my TV. iTunes content (even audio only) will not play on the Westinghouse.

Any suggestions (other than buy a new TV)?