There is a (very) thin space that shouldnʼt be there between the 1f44d
and the '|' on the line that has the FE0F (and since it follows the
value of glyphless-char-display-control, I donʼt think
it comes from the shaping engine).

but

(set-char-table-range
 composition-function-table
 #x1F44D 
'(["\U0001f44d\ufe0f" 0 font-shape-gstring]))

gives me this, where the two '|' align perfectly.