Once the entire logistical chain is fully automated the teamsters will have much less power. After all, if you don't need workers it doesn't matter if they strike.
A strike seems like the perfect time to introduce automation.
The only thing you're not including in this equation is votes. Union leaders simply need to convince lawmakers that it's in their best interests to pass favorable legislation limiting the adoption of new technologies. It's certainly been done before.
This is where America's organization as a collection of states is helpful. At least one or two states will be willing to let automation take over once it's developed, and it's effectiveness there can become leverage to spread it to other states.
That seems to assume a (almost) simultaneous switch from manual to automatic. In reality, it would probably be done as a small test case to see how well it works and be expanded slowly. A strike during this process can still be damaging.