recreating curved frame

If you do the laminations, 1/4” should work and be very strong. A few tips...do a dry run first. Make it a little long so you don’t have to worry about the ends lining up during gluing. If in your pictures the top old board is what you need, make a jig from it, not adding to it like the photo. Have plenty of clamps. Use titebond 2 or 3 or Extend if you can find it. Put it on quick with a 2” paint roller. Clamp from center out in both directions. Have a helper if possible. Let it set a day or two. It may spring back a little so possibly over bend just a hair to start. Have fun.

Yep, laminating is probably the best way to go. However, the woodworker in me is salivating at the opportunity to make a steam bender. It looks pretty easy to do with PVC and a clothes steamer and duct tape. Still, I'd have to build bending forms to match the target curves.

Either method will be superior to the Kerfing method because those short lengths will definitely split when receiving nails or screws.