The following gets me close to what I am looking for. Adding \setupinterlinespace[1pt] seems to suppress the addition of space between the lines of the header. Changing the interlinespace only seems to have an effect above some threshold related to the font size. For example, changing 1pt to 3pt has no visible effect. Changing 1pt to 10pt adds space between the first and second lines only. Changing 1pt to 100pt adds space between lines 1/2 and 2/3. I would prefer to have precise control over the space between the lines, but I can live with this (it is much better than the large spaces which appear of you remove the \setupinterlinespace declarations).
This still leaves the problem of calculating the header height provided in \setuplayout so that body text is a set distance from the header for arbitrary font size, number of lines, and text contained in the header.
Thanks, Neal
\starttext
\setuppapersize[letter]
\setuplayout[topspace=0.20in,height=10.60in,header=28pt,footer=0.32in,headerdistance=0.03in,footerdistance=0.03in,backspace=0.3in,width=7.90in]
\setuppagenumbering [location=]
\define\headerframe{{\framed[frame=on,strut=no,offset=0.0pt,height=fit,width=7.9in,align=middle]{{\switchtobodyfont[24.00pt]\setupinterlinespace[1pt] eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee\par}
{\switchtobodyfont[10.00pt]\setupinterlinespace[1pt] eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee\par}
{\switchtobodyfont[24.00pt]\setupinterlinespace[1pt] eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee\par}}}}
\setupheadertexts[\headerframe][]
This is the body text.
\stoptext