Yea, this is a weak spot in Chart Supplement, and has been for decades. A lot of times it falls under, as some have pointed out, "local knowledge". If I'm flying into someplace unfamiliar, I always ask ATC what the best contact point is on the way out.
I guess the hierarchy of clearance delivery sources at uncontrolled fields is:
Dedicated RCO or frequency usable on the ground
Phone direct to responsible ATC facility (increasingly common option, number will be listed in the CS)
Simplex frequency and receive over a VOR through flight service (a rapidly diminishing option)
Phone call to the national clearance delivery number.
The problem is that the Chart Supplement doesn't really make it clear the exact nature of the frequencies / contact points.
Even on the best of days, the phone call to Leidos FS is not the optimum. The several times I've used it, it required a significant back and forth to the person on the phone to make it clear where I was and what I wanted, and the ultimate result is some kind of weird 3 way call with the ATC facility. It's NOTHING like getting a clearance through Flight Service in the pre-L/M days. Some of the time they just gave me a phone number to call direct. I try to avoid the national CD number and only use it as a last option.
They've cleared some of the hurdles with ATC to publish the numbers for clearances, and hopefully that paves the way to some kind of CPDLC for GA that would make this issue go away.