I am pleased to report success with my latest attempt. I actually did two burns as a learning experience. The base file coming from EyeTV was Toasted once with all Toast settings at "Auto". The burn it produced seemed kind of "squeezed" left-to-right for width when played back in 4X3 mode even though the EyeTV file recorded it from U-verse's "standard definition widescreen" video output setting.
I didn't use U-verse's "4X3 standard definition" output setting for the transfer into EyeTV as I had originally planned when I saw there was a standard definition widescreen option for video output on the U-verse box. Since the file was 16X9 when played back in EyeTV after recording from U-verse the "squeezing" surprised me. So, I did a second Toast burn with specific settings in Toast advanced options specifying a 16X9 resolution and the second burn was better and though not full widescreen on playback, it was wider side-to-side and was a better viewing experience. And, I could use the Sony TV's settings to "wide zoom" the file when playing back to fill to get full widescreen. With the first burn with Toast's "auto" settings, the television "wide zoom and zoom" settings had no effect on the content. Both Toast processed files did have a moderately long "encoding" period, so I'll experiment again with a forced no re-encode as you suggested and see what happens.
I just noticed your signature file so you might be interested to know that the film I have been working with is "Magic Trip" the Hollywoodized version of Ken Kesey and a the Merry Pranksters' legendary 1964 transcontinental bus trip which I was a part of back in the day. Though at the time of the trip I was living and working in Ohio, I came out to Eugene after the trip and stayed for nearly 20 years before coming back to the Midwest in the mid-80's. I am planning a sentimental journey to Eugene next month. I had hoped to come in July during the Oregon Country Faire but took a fall and screwed my back just as I was planning to leave. Six weeks and lots of Physical Therapy later, I'm ready again. The trip is also to check out the housing market as I contemplate a return for my impending dotage as it were. I love Eugene and have missed these past couple of decades while toiling in the Big Blue fields of Ann Arbor, MI.