Thanks to the many suggestions and ideas. I tried 'em all, and the one
that worked was to minimize the length of coax between the little UHF
circular antenna and the converter box. The converter box itself gives
off a little RF but only up close, similar to most modern electronic gear.
However, when you hook up an external antenna, the digital converter
apparently radiates the noise over the antenna feed cable. I had an
elaborate switching network for when I utilized more than one antenna, and
bypassing all that got rid of the noise.
Hope this helps someone else faced with this problem! "Hash" is a gentle
descriptor - it was more like a solid high-pitch whine/buzz which
precluded DX on the lower band. Fortunately, peaceful coexistence has
been restored between my DXing and the girls' TV viewing (in fact, the
signal on the TV is a little better!).
Thanks again - Kevin S
Bainbridge Island, WA