my $match = "\Q" . join ("\E|\Q", keys %translate) . "\E";
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There's a problem here. In interpolated strings, the  \Q and  \E escapes act as interpolation 'controls' (if that's the right term) and softly and silently vanish away. Except for raising a ruckus, using non-interpolating strings doesn't help matters:

>perl -wMstrict -le
"my %translate = (
   'tr??u++e' => 1,
   'fa+l?se'  => 0,
   );
 ;;
 my $match = qq{\Q} . join(qq{\E|\Q}, keys %translate) . qq{\E};
 print qq{'$match'};
 $match = qr{$match};
 print $match;
 ;;
 my $mooch = '\Q' . join('\E|\Q', keys %translate) . '\E';
 print qq{'$mooch'};
 $mooch = qr{$mooch};
 print $mooch;
"
'tr??u++e|fa+l?se'
(?-xism:tr??u++e|fa+l?se)
'\Qtr??u++e\E|\Qfa+l?se\E'
Unrecognized escape \Q passed through in regex...
Unrecognized escape \E passed through in regex...
Unrecognized escape \Q passed through in regex...
Unrecognized escape \E passed through in regex...
(?-xism:\Qtr??u++e\E|\Qfa+l?se\E)
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Update:

There's another problem. The unordered keys of a hash are being used to build an ordered regex alternation, which always matches the first alternation match found even if there is a longer match in a subsequent alternation possibility. The problem may not bite in this application because the strings being searched (per the example in the OP) seem to be nonword-bounded words (and throwing in some  \b assertions would probably help, as Your Mother points out in Re: timtowtdi but which is the [quote fingers]best[/quote fingers]), but in another case (and if the longest match is, indeed, desired) it might:

>perl -wMstrict -le
"my %xlate = (
   A    => '1',
   AA   => '2',
   AAA  => '3',
   AAAA => '4',
   );
 my $mooch = join '|', keys %xlate;
    $mooch = qr{ (?i) $mooch }xms;
 my $match = join '|', reverse sort keys %xlate;
    $match = qr{ (?i) $match }xms;
 print $mooch;
 print $match;
 ;;
 my $s = 'xAxAAxAAAxAAAAx';
 print qq{'$s'};
 $s =~ s{ ($mooch) }{$xlate{ uc $1 }}xmsg;
 print qq{'$s'};
 ;;
 $s = 'xAxaaxAaAxaAaAx';
 print qq{'$s'};
 $s =~ s{ ($match) }{$xlate{ uc $1 }}xmsg;
 print qq{'$s'};
"
(?msx-i: (?i) A|AA|AAAA|AAA )
(?msx-i: (?i) AAAA|AAA|AA|A )
'xAxAAxAAAxAAAAx'
'x1x11x111x1111x'
'xAxaaxAaAxaAaAx'
'x1x2x3x4x'
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Since the OP seeems to be looking for longest words and word phrases, I think I would go for the  \b-elt-and-suspenders approach of something like:

>perl -wMstrict -le
"my %xlate = (
   'string a' => '3',
   'string b' => '2',
   true       => '1',
   false      => '0',
   tt         => '22',
   ttt        => '33',
   );
 my $xl = join '|', map { quotemeta } reverse sort keys %xlate;
    $xl = qr{ (?i) \b (?: $xl) \b }xms;
 ;;
 my $s =
   'vv TTT ww TT String A xx sTrInG b xtruex True yy FALSE zz';
 print qq{'$s'};
 ;;
 $s =~ s{ ($xl) }{$xlate{ lc $1 }}xmsg;
 print qq{'$s'};
"
'vv TTT ww TT String A xx sTrInG b xtruex True yy FALSE zz'
'vv 33 ww 22 3 xx 2 xtruex 1 yy 0 zz'
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