Trouble running a wire just inside the headliner along the windshield

I need to run a cable up the driver side A pillar and then along the edge of the headliner toward the rear view mirror.

I got the wire up the pillar and I had no trouble tucking the wire under the edge of the headliner along the windshield - mostly. From the pillar until about 2/3 of the way toward the mirror the wire tucked in just fine. But that last third it seems the headliner is attached to the windshield right to the edge preventing me from tucking the cable in there.

Is there a reasonable solution to getting the wire tucked in along the edge of the headliner within vicinity of the mirror?

 

I ran a wire for a cell booster antenna up there and didn’t have any issue. I used a trim removal tool to tuck it in.

 

Yes a trim removal tool will create enough of a gap to get the cable in there.

 

But the trouble spot I'm referring to is actually attached to the glass unlike the first 2/3 where I could pull the edge of the headliner away just enough. Are you guys suggesting that I use a trim tool to break that seal?