I have to specify it's for broadcasting [...] doesn't that change the nature of the socket?

I think it simply allows it to broadcast and receive broadcasts.

What catches my eye is that you chose to connect to INADDR_BROADCAST. Connecting a UDP socket (i.e. specifying PeerAddr) means you can only receive from the address to which you connect. What does it mean to connect to INADDR_BROADCAST? ( Can only receive broadcasts ) Do you have to connect to INADDR_BROADCAST? ( no ) Will test tomorrow.

I don't see a method in IO::Socket::INET or IO::Socket that lets me change the Broadcast flag to 0 after I send a broadcast.

Since Broadcast=>1 does

$sock->sockopt(SO_BROADCAST,1)
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the approach would be

$sock->sockopt(SO_BROADCAST,0)
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But again, I don't think this is necessary.