At the moment I don't see a way to hand an existing socket object like the one returned from $ssh->open_tunnel to DBD::mysql.

It seems like what you want is the equivalent of ssh -L, but looking into the documentation of Net::OpenSSH, I'm not sure that's supported, as it has this to say about tunnels:

Under the hood, in order to create a tunnel, a new ssh process is spawned with the option -W${address}:${port} (available from OpenSSH 5.4 and upwards) making it redirect its stdio streams to the remote given address. Unlike when ssh -L options is used to create tunnels, no TCP port is opened on the local machine at any time so this is a perfectly secure operation.

You might be able to DIY using the ssh_opts option. I'm not an expert on Net::OpenSSH so I can't say if there's a better way, but this worked for me (tested with a different server, not MySQL, but that shouldn't make a difference):

use Net::OpenSSH;

#$Net::OpenSSH::debug |= 16;
my $ssh = Net::OpenSSH->new($host);
die $ssh->error if $ssh->error;
my $pid = $ssh->spawn({ssh_opts=>'-L 127.0.0.1:12345:127.0.0.1:3306'},
+ 'cat');
die $ssh->error if $ssh->error;

# connect to remote MySQL via TCP at local 127.0.0.1:12345
sleep 10; # do your work here

print "Ending...\n";
kill 'INT', $pid;
waitpid ($pid, 0);
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