If it gets big enough, it could cause a soft-fork. But that's a much different/smaller problem than a hardfork, and unlikely to occur (since miners would presumably get their act together before it got to this point).
If half the network decides that blocks containing SD transactions are valid, and the other half decide they are invalid it would indeed be a hard fork.
Notice I never suggested to consider them invalid. Just not relay them.
There's no guarantee that it would go your way either. The majority of the network might just continue processing those transactions and ignore your blocks until you get your act together.
You mean Bitcoin's way. My miners are just doing their job filtering out spam, like they're supposed to as part of the Bitcoin system.
And if you start trying to force miners to accept transactions, you're breaking Bitcoin.
In this particular case, you'd in effect be creating a SD tax on miners.