I think your main problem is that you are using async. It is useful for small blocks of code , but once the subroutine gets to your level of complexity, it is better to name it and use threads->create.

Once you make that change, it then becomes clear that you have a third option to immediately calling either join() or detach(). You can simply save the thread handles and defer that until later. See how you get on with this:

#!/usr/bin/perl
use strict;
use LWP::UserAgent;
use HTTP::Request;
use threads;
use threads::shared;
use strict;

my %clients :shared;

sub doit{
    my $mac = shift;
    my $macAuthURL = "https://XXXXXXXX/api/macCheck/";
    my ($request, $ua, $response, $respcon, $rval);
    my ($returnkey,$returnval);

    print "MAC: ".$mac."  Contacting $macAuthURL$mac.\n";
    print "This is ".threads->tid()."\n";

    # Wrap call to API with eval
    eval {
        local $SIG{ALRM} = sub { die "Alarm\n" };
        alarm(16);
        my $macr = $macAuthURL.$mac;
        $request = HTTP::Request->new(GET => $macr);
        $ua = LWP::UserAgent->new();
        $response = $ua->request($request);
        $respcon = $response->content();
        alarm(0);
    };

    # We check the response object's status
    if($response->status_line =~ /^500/ ){
        print "MAC: ".$mac."  Network Delay/Error.";
        { lock (%clients); $clients{$mac} = 0; }
    }
    print "MAC: ".$mac." Server response: $respcon \n\n\n" ;

    # All OK - Ensure that sent mac is returned back on success.
    if( $response->{_rc} == 200 ){
        $response->{_content} =~ s/[\{\} \"]//g;
        ( $returnkey, $returnval ) = split(/:/,$response->{_content},2
+);
        print "MAC: ".$mac."  returned with status: $response->{_rc} "
+;
        if( $mac eq uc($returnval) ){
            { lock (%clients); $clients{$mac} = 1; }
        }
        else{ # Malformed URL
            { lock (%clients); $clients{$mac} = 0; }
        }
    }
    else{
        { lock (%clients); $clients{$mac} = 0; }
    }
    sleep 1;
}

# A list of MACs extracted from DHCP leases.
my @maclist = qw (
    7D:6D:62:C6:B4:3D 01:12:79:3E:14:2E 80:27:E4:EA:60:74
    E8:06:88:7F:8C:83 01:26:08:E8:B6:5D 34:15:9E:5D:E6:49
    03:1E:64:CE:25:88 01:0C:29:3F:67:1B 01:22:69:76:5D:F4
    64:B9:E8:10:BF:20 01:1D:FE:D4:7F:E0
);

my @threads;

foreach my $mac (@maclist){
    push @threads, threads->create( \&doit, $mac );
}

$_->join for @threads;
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