You're on the right track. A concave face is as forgiving as you can get for a difficult material like PEEK. How confident are you that both the rim and its corresponding seat are free of tiny scratches? If unsure, color both parts with a Sharpie and apply a light abrasive like J-B (or a thick oil and diatomaceous earth slurry) and spin them together lightly for a few seconds. If the Sharpie marking isn't removed neatly on both the poppet and valve seat, the problem area should be clear.
Otherwise it's most likely as Biohazardman indicates, something is slightly out of square. The first PEEK poppet I ever made with caveman tools (drill press) was that way. To address it, I made a simple jig. It's just a 1-inch scrap of hardwood with a hole just big enough for the stem to pass through.
Then I used a hollow punch to knock out a bunch of holes in a piece of 220 grit sandpaper, which you see in the photo. From there, it's just a matter of putting the stem through the sandpaper and the wood block, and grabbing the stem from the back side with a drill and spinning it against the sandpaper to true it up. PEEK is tough as nails so it may take a while. Then a little time with 400 and 600 grit to smooth it.
Lastly, I lapped it to the valve with a light abrasive slurry using the Sharpie trick to gauge when I had done enough.
Naturally it's best if the hole you drill in the jig is perfectly perpendicular so do it on a drill press if possible, but even if it isn't perfect, it will still work. It will just make the poppet face slightly convex but still true to the stem.