You do have a few other choices here, too. Depends on wht tools youhave and how much time you want to spend on one task, instead of another.

You could take a strip which has bead and cove edges, and rip it in half. That gives you half a strip with a bead edge and half a strip with a cove edge. You can then slip your pinstripe material (with square edges in the middle of these half-width strips. Depending on the situation with twisting and bending you might want to glue these together on a flat bench covered with wax paper, which would give a nice flat joint, and a wider than average strip with a pinstrip in the middle of it. I have a lot of black walnut chunks on the firewood stack which I can split, and rip into small pieces. Sandwiching several 1/8" pieces of walnut which are only 15" to 18" long between halves of a cedar strip would give me a way to use those short pieces easily. I could even do a dashed line of short pieces--perhaps an inch in poplar, followed by an inch of walnut, sandwiched in the middle of that cedar strip. It is a nice way to use small scraps of exotic woods.

Or, take advantage of the flexibility of the very narrow strips and glue them in place on your forms, one at a time. This works really well in areas with sharp bending.

You can do all your stripping without the pinstripes, and then go back and cut a groove for the pinstripe material to fit into. This can be time consuming, and tricky to do with a router, but it gives you the chance to do pinstripes that cut across several strips. If you are looking for a design which has diagonals, or curved pinstripes this is your "better" option. If you are using materials other than wood for your pinstripes, such as Malcolm Sweitzer does with inlayed abalone, or if you use a liquid resin inlay, you'll be routing a gooove for them.

PGJ