Sorry for the prolonged replies, everyone!
I'm now at the JFK T4 SC, got in without any pushback. The benefit is definitely there for transcon paid J at the JFK SC.
As for the DCA SC and transcon J, interesting. I did travel a few times on paid transcon BE in the past, and entered DCA's SC before without a problem. When asking for D1 transcon advice earlier this month, I did get this response:
Originally Posted by
ATOBTTR
B) You will have SkyClub access at DCA. Your whole itinerary should display to the agent when you check-in, and he/she should see the JFK-SFO leg. If you get any flack when you check-in at the club, present you D1 boarding pass for JFK-SFO.
So, based on those factors, I had a reasonable expectation I would get entry automatically at DCA. MSPEconomist is right, though: the DL website doesn't show DCA as a SC when selecting transcontinental.
The DCA SC was surprisingly very sparse and empty this morning, which is why they might've let me in.
DL really should clear this up, and make it clear upfront that paid transcon D1 customers only get access at JFK, SFO, and LAX. Right now, it seems to be ambiguous and mostly YMMV.