I also like using laminated linings as it's much easier and far less expensive to find wood that is suitable for laminated linings than it is to find spruce or mahogany for kerfed ones. I bought a 3 meter long board of Hoop Pine for $5. Enough to do dozens of instruments.
First off, I ripped some Hoop Pine into strips and ran them through the drum sander to end up with 3 strips 1.4 -1.5 mm thick. Gives you a finished lining 4.2 to 4.5 mm thick.

You can also see the bending form and outside mold that, as well as some clamps.
I give each of the strips a little bend on the hot pipe, just to help them into the waist of the mold without fracturing.

Then I brush each of the mating surfaces with hot hide glue, wrap the strips in baking paper so the don't stick to the form, and clamp them up. No pictures of the glue up as I had to move reasonably fast.

Let dry over night preferably, then you will end up with something that looks like the piece on the left. I then trued up a face, and slice off 10 mm strips on the band saw.

I run them past a round over bit in my router table, then trim to length and glue in with some more hot hide glue.

It makes very stiff rims, and does look good in my opinion. Same process for any size instrument. You can even get really fancy and use contrasting woods to give a stripe effect.