I'm aware of people who got SC as well as HC judicial internships without any connection, you just need to pester the PS or the LRs long enough. Try at a few places. In HC obviously it's a bit easier since you can get easy entry. I've even heard of people trying to go to the judges' residencies to drop off their application. While having a connection might help, you can get a judicial internship directly as well. I'd also suggest asking someone who has already interned there for a reference or the contact of the PS.