I think that it is safe to say that you would be safer with your climbline cinched around the spar and your lanyard wrapped around the spar ABOVE the rigging. It prevents the possibility of the rigging sling sliding down onto your life-support gear. You prevent the rigging rope from running over your climbline and lanyard with the possibility of damage, or just pinning your gear in place.
Remember to place your kerf cuts below the hinge in case the side of the hinge tears down or there is a minor barberchair.
If there is a major barberchair (more likely if you are taking a leaning top) and you are around the trunk with a flipline, you/ your harness and your person within the harness are part of the circle around the pole. If there is a major barberchair and split, you get sucked into the trunk and smashed, especially dangerous if you have left any stubs on the tree. You can address this by repositioning your lanyard from you D-rings to your bridge, and have the climbline on your bridge. Sometimes I'll keep my weight on my cinched climbline with GriGri SRT, and clip the snap of my flipline back to the running/ standing part of the flipline (between the adjuster and the tree). This keeps me from only relying on my bridge with no back-up.
As for your more specific question, if you are choked off to the tree, you don't have to worry about staying on your spikes in a more vulnerable position. With the choked climbline, you can pull your spikes out if you see the log coming at your feet.
This should not be happening in the first place. Call and Respond with your groundman: "I'm going to facecut, then backcut this piece. You let it run clear of me and give it a soft catch." Response:" Facecut. Backcut. Drop it clear of you. Soft catch! Ready!"
I was working on a lombardi poplar and for no good reason the groundie thought that I wanted the piece stoppped dead/ snubbed off. He shockloaded the rigging which was on the stem that I was relying on for my life. I was not a happy camper. If you/ groundie are new to it, be extra explicit on what you want, and what they understand that you want. After working together for a while, you will be able to be less explicit. The groundie should understand what the set-up will be and double check from the ground. Too many people have had a climbline still attached to the piece being dropped and caught. The groundie should double check, and let you know if it looks good or if you should triple check before cutting, or if he can't see the set-up.
Good question. Keep asking them, and reading old posts. Be Safe.