\input basic
\chcode'100←4

\def\mash #1\endfmt{\gdef\result{}\workon#1"\tricky}
\def\workon#1"#2{\if T\test#2\tricky{
           \xdef\result{\result#1}\gdef\remainder{}}
  \else{\xdef\result{\result#1{$ ## $}}
          \gdef\remainder{\workon#2}}\remainder}
\def\test#1\tricky{\gobble#1TF}
\def\gobble#1#2{}
\def\tricky{T}

\def\array\colfmt#1\endfmt{\mash #1\endfmt}

\def\rows#1{\vcenter{\halign{\tabskip 0pt\result\cr #1}}}
\def\endrow{\cr}

% now you say \array\colfmt {preamble with " for {$ # $} and @ for ⊗
% and e.g. \rows{x1@x2@x3\endrow y1@y2@y3\endrow}