One thing I don't entirely understand is whether having an EU-based server provided by an US company (Rackspace, AWS, Digital Ocean, you name it) makes any difference at all.
No one can say - although at the moment you can be sure they are subject to US intercept orders.
The companies are incorporated in the US, so subject to US law. But the physical servers are located in other jurisdictions, and sometimes US law conflicts with that law.
In practice, so far I suspect that the US law has won out, because other jurisdictions haven't known to fight it. In the future that might change, but... secret orders supported by secret laws enforced by secret courts can be pretty hard for other jurisdictions to fight.
A server that is located in the EU is almost certainly owned and operated by a EU-based legal entity that is a wholly owned subsidiary of the US parent. So strictly speaking you would be getting your services from a EU company that is owned and controlled from the US but that is subject to all the relevant local laws.
The companies are incorporated in the US, so subject to US law. But the physical servers are located in other jurisdictions, and sometimes US law conflicts with that law.
In practice, so far I suspect that the US law has won out, because other jurisdictions haven't known to fight it. In the future that might change, but... secret orders supported by secret laws enforced by secret courts can be pretty hard for other jurisdictions to fight.