Thanks for all the advice everyone. It certainly made me feel like a dunce after spending so much time getting everything squared up and plumb on my press.
And yes... I went with TOTWs tool/part list recommendation for the 1/4-32 white lightning liner. That 1/4" csink definitely is too small.
I talked to the nice gentleman at MBS. His white lightning liners ARE from Chambers and said they're 82* countersinks. So even though I had to go with a SS version, I ordered a 5/16 from him because he's given me plenty of help and parts, it's generally one day shipping from him to me, and I'm not blueing or browning my barrel so it shouldn't stand out too terribly much. I also have a 3/8" 82* csink on hand that works pretty well. So I'll just redrill/tap the hole in the next couple of days and be extremely careful with the csink. I'm having to make some concessions on my build due to trying to be able to hunt with it in the first half of November. I have some eye health issues that could leave me unable to hunt in the future so I'd like to be able to use it at least once. That's why quick shipping is important and a SS liner will be just fine. I'll go back over the winter and add some of the other items to the rifle that are needed like a patchbox, maybe forestock molding if I don't get there, and maybe a cheek piece eagle inlay. I'll have to refinish it after installation of these, but that's ok.
As a sidenote, I read somewhere that DPhariss and I think Dennis glazener recommend not tapping the hole all the way through into the bore so that there is a shoulder at the bottom and it's less likely to collect fouling in exposed threads that would be there if you tap all the way through. That sounds nice, so I may try that if it is worth doing.