J,
How about not doubling $$ if NoVarsInStrings is on.
code:
break on

dim $c, $out
$     = setoption("NoVarsInStrings","on")
$n    = 1
$c    = 1
$s1   = "string " + $n
$s2   = "string 2"
$s3   = "string 3"
$out  = ""

while execute("exit vartype($s" + $c + ")")
    $ = execute("$out = $s" + $c)
    $out ?
    $c = $c + 1
loop

get $
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