I have another answer I can live with a little easier. I wrote another
proof of concept script wherein the MainWindow is kept as mentioned before.
It looks like I can create and destroy Toplevel windows as I need to,
while keeping the MainWindow withdrawn.

This works without getting a segmentation fault:

sub service_for_mw_button_press {
  my ($mw) = shift;
  my $top_level = $mw->Toplevel
[download]

and then later, when I no longer need the $top_level,

$top_level->destroy;
undef($top_level);
$mw->deiconify;
$mw_raise;
[download]

This idea, plus a redesign to make the real program an event driven
design from the beginning, should do the job. Thanks for all of your
help.