To the comment
@ the comment “many videos online of people demonstrating ways to pitch a tarp, the only people (outside of Philmont) I see doing this are hammock users.”
Lots of other folks sleep under tarps and your hammock videos are not helping much since they are tying off to trees. My normal backpacking shelter is a tarp. You can search past BPL articles for many articles about pitching shaped tarps. You are using a “flat tarp” but the principles are the same.
It looks like you bought a tarp with webbing so you should not need to 1) use any adapter with the webbing attachment to the pole or 2) use a cord under the ridge line.
If your poles are slipping, after tying the cord to the webbing, attach the same cord with a timber hitch or several clove hitches to the pole, then run the cord to the ground. There are multiple photos on BPL of how this works. If your stakes holding the ridge line poles are pulling out, attach a second cord between the pole and the ground to you have two attachment points at an angle of about 30 or 40 degrees.
With a high quality silnylon tarp (which is very strong) if you have enough tension on the two ends respectively, you do not need a cord under the ridge line, and the use of such a cord in my experience makes adjustments to and knot tying at either end more complicated.
If this description is not making sense, send me a message and I can send you some photos.