Kind of hackish... but as the start handler is being called before the text handler, you could store the tag name in a global variable, which you can then use in the text method to decorate the content as desired:

...
my $tagname;
sub start {
        my ($self, $tag, $attr, $attrseq, $origtext) = @_;
        $tagname = $tag;  # store tag name for later use

        if ($tag =~ /^span$/i && $attr->{'class'} =~ /^main-content$/i
+)
        {
            # set if we find <span class="main-content"
            $content_flag = 1;
        }
  }
sub text {
        my ($self, $text) = @_;
        # If we're in <H1>...</H1> or
        my $tagged_text = $text !~ /^\s*$/ ? "<$tagname>$text</$tagnam
+e>" : $text;
        if ($content_flag)    { $main_content    .= $tagged_text; }
}
...
[download]

Output:

    <bold_text> Here's the body 1 </bold_text>
    <p> para1 </p>
    <p> para2 </p>
[download]

(Might need some further tweaking (like the $text !~ /^\s*$/ ? ...) to handle edge cases — but you get the idea.)