Just to test if it would bring speed (which I did not expect), I fiddled with pack and unpack. Before doing the hard part, I looked at the speeds halfway. It is not worth pursuing.

I also looked at Inline::C, and it is slower than your perl code (and I already optimized the stack stuff)

$ cat test.pl
use 5.016;
use warnings;

use Inline "C";
use Benchmark qw( cmpthese );

my $n = 0x80061861;
my $x = 10000;

sub andshift
{
    my ($top14, $nxt6, $mid6, $bot6);
    for (1 .. $x) {
        $top14 = ($n & 0xfffc0000) >> 18;
        $nxt6  = ($n & 0x0003f000) >> 12;
        $mid6  = ($n & 0x00000fc0) >>  6;
        $bot6  = ($n & 0x0000003f);
        }
    return ($top14, $nxt6, $mid6, $bot6);
    } # andshift

sub packunpack
{
    my ($top14, $nxt6, $mid6, $bot6);
    for (1 .. $x) {
        ($top14, $nxt6, $mid6, $bot6) =
            unpack "A14 A6 A6 A6", unpack "B32", => pack "N" => $n;
        }
    return ($top14, $nxt6, $mid6, $bot6);
    } # packunpack

sub inlined
{
    my ($top14, $nxt6, $mid6, $bot6);
    for (1 .. $x) {
        ($top14, $nxt6, $mid6, $bot6) = split14666 ($n);
        }
    return ($top14, $nxt6, $mid6, $bot6);
    } # inlined

say for andshift ();
say for packunpack ();
say for split14666 ($n);

cmpthese (-1, {
    andshift   => \&andshift,
    bitstrings => \&packunpack,
    inline_c   => \&inlined,
    });
__END__
__C__
void split14666 (int n)
{
    Inline_Stack_Vars;
    Inline_Stack_Reset;
    EXTEND (sp, 4);
    mPUSHi (((unsigned int)n & 0xfffc0000) >> 18);
    mPUSHi (((unsigned int)n & 0x0003f000) >> 12);
    mPUSHi (((unsigned int)n & 0x00000fc0) >>  6);
    mPUSHi (((unsigned int)n & 0x0000003f)      );
    Inline_Stack_Done;
    } /* split14666 */
$ perl test.pl
8193
33
33
33
10000000000001
100001
100001
100001
8193
33
33
33
            Rate bitstrings   inline_c   andshift
bitstrings 121/s         --       -52%       -74%
inline_c   250/s       108%         --       -47%
andshift   470/s       290%        88%         --
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