One of the TVs I watch cable on is an ancient Sony Wega 36XBR450. It's a 4:3 TV that supports 480p and 1080i (in letterbox), and has component video inputs (YPbPr).
My old cable box (RNG110) would switch video output based on the input signal. SD content would be output at 480p, and HD content would be output at whatever HD resolution it was set to (1080i in this case). It works well for this TV.
From everything I've seen, it looks like the X1 box does not support this. Can someone definitively confirm that? If so, sounds like I need to stick with the RNG110 on this TV until I ditch the TV.
Your analog television is way past being a "White Elephant".
The local "over the air" stations have all moved to digital equipment and the signal output sent to cable channels may have changed. Do you get any local channels at all using your antenna?
If so, how does that picture look on your analog television? Since a 720p (widescreen) television can be bought for about $75. you would be much better off giving up using the old Sony tv.