A thin strip of wood lath cut to fit and painted the same color as the trim would almost disappear completely.

how would you attach it?

You could attach the wood strip with a couple of L brackets, but I think it looks fine like it is.

I removed all the mini blinds that came with our house. They had a narrow wood valance that covered the head rail and were attached with a special plastic clip. You might be able to find some ready made ones that fit your blinds.

Here you go, just looked it up and you can get spare parts, see link.

Here is a link that might be useful: Mini blind valance clips

You can also get valance clips on Amazon; I just ordered several packs last week, with free shipping too if you are a Prime member. Link below.

Here is a link that might be useful: Amazon Valance Clips

I like it as it is but the narrow lath painted like your woodwork would work. Maybe use double sided foam tape to secure it to the head rail.

grandmaof3 I like that idea. Reminds me of the 3m velcro or regular command strips that would work too - no adhesive residue.

Thank you, everyone, for your creative ideas!. You have given me great direction and I should be able to come up with a solution. Thank you for your generosity of time. I do appreciate it!