I like your idea Ray.
Take it off keep the hood together, prime all parts reassemble and then paint.
Here is my thought.(not that I know anything)
but all surfaces will at least be cleaned well, and primered. Most surfaces will get paint too.
If you leave the strip on I see some areas not getting cleaned/derusted and the painting over this mess causing some future problems.
But what do I know.
I haven't even seen myhood in 2 years.