Took a stab at Option 1; need to test it more but looks promising. 
my $dom = XML::LibXML->load_xml(string => <<'END_XML');
<?xml version="1.0"?>
<office:document-content office:version="1.2"
    xmlns:office="urn:oasis:names:tc:opendocument:xmlns:office:1.0"
    xmlns:text="urn:oasis:names:tc:opendocument:xmlns:text:1.0">
<office:body><office:text>
<text:p text:style-name="P1">
    Fo<text:span text:style-name="T1">o<text:line-break/>
    B</text:span><text:span text:style-name="T3">a</text:span>
    <text:span text:style-name="T5">r<text:line-break/></text:span>
  </text:p>
<text:p text:style-name="P3">
  TEST is a &apos; real test.
  </text:p>
</office:text></office:body>
</office:document-content>
END_XML
my $xpc = XML::LibXML::XPathContext->new($dom);
 $xpc->registerNs('office',
     'urn:oasis:names:tc:opendocument:xmlns:office:1.0');
 $xpc->registerNs('text',
     'urn:oasis:names:tc:opendocument:xmlns:text:1.0');

while (1) {
    my ($lb) = $xpc->findnodes('//text:line-break') or last;
    die "can't handle <text:line-break> with children: $lb"
        if $lb->hasChildNodes;
    my ($a) = $xpc->findnodes('ancestor::text:*[1]',$lb)
      or die "failed to find ancestor of $lb";
    my ($a_a) = $xpc->findnodes('ancestor::*[1]',$a)
      or die "failed to find ancestor of ancestor of $a";
    my $clone_a = $a->cloneNode(0);
    my $nextSibling = $lb->nextSibling();
    while ( $nextSibling ) {
        my $currentSibling = $nextSibling;
        $nextSibling = $currentSibling->nextSibling();
        $currentSibling = $a->removeChild($currentSibling);
        $clone_a->addChild($currentSibling);
    }
    $a->removeChild($lb);
    $a_a->insertAfter($clone_a,$a);
}

print $dom;

[download]
Which produces 
<?xml version="1.0"?>
<office:document-content xmlns:office="urn:oasis:names:tc:opendocument:xmlns:office:1.0" xmlns:text="urn:oasis:names:tc:opendocument:xmlns:text:1.0" office:version="1.2">
<office:body><office:text>
<text:p text:style-name="P1">
    Fo<text:span text:style-name="T1">o</text:span><text:span text:style-name="T1">
    B</text:span><text:span text:style-name="T3">a</text:span>
    <text:span text:style-name="T5">r</text:span><text:span text:style-name="T5"/>
  </text:p>
<text:p text:style-name="P3">
  TEST is a ' real test.
  </text:p>
</office:text></office:body>
</office:document-content>

In reply to Re^2: fix ODT files with line breaks looking poor by melutovich
in thread fix ODT files with line breaks looking poor by melutovich

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