If you wanted to get back to black based paints without getting a black the easiest way would probably be through pairing Eko with your splash Layla.
You'd have blue paints and blues the first generation but you could breed a blue paint daughter back to Eko and get 25% black based paints, 25% blue based paints, 25% black, and 25% blue.
If you bred a blue paint son back to Layla you could get 25% splash paints. I've only seen them a few times but the ones I saw I thought were very pretty! I actually managed to track down some of the pictures I found of a couple in the american paint silkie thread here on BYC. They are shown in post #1127
https://www.backyardchickens.com/threads/the-american-paint-silkie.429754/page-113
I'd pick splash if you don't have any blue or black females as it shouldn't introduce any of those recessives that can be so tough to keep track of and breed out (partridge and recessive white).
I'm not sure if you need more red then a partridge typically has but paint over red partridge will start giving you a percentage of red pyle like chicks after the second generation I think. Maybe you'd get some more buff colored pyle like offspring with regular partridge?
Hmmmm I'm not sure what whoever said that meant about the blacks but I can think of maybe two possibilities.
1st possibility is they were referring to how some breeders will refer to a line of blacks that has been breeding for multiple generations and only produces black as "true blacks". The blacks you get from things like blue/black/splash or paint pens are usually blacks too. Occasionally there are anomalies with the blacks from paint or really dark blues that just look black out of blue/black/splash pens. Generally though black birds produced from pens that have other colors are considered blacks as well hence why "true blacks" as a term can annoy some people. They may view it as there is no such thing as a "true black silkie" a black silkie is just a black silkie no matter the background.
2nd possibility may be referring to the "base" black silkies are made on. While many black chickens are made with the E (extended black) base, silkies are a breed that is often thought to perhaps be made on another base or bases. You can make a black bird using multiple different bases but E is one of the easier ones that requires less modifiers.
I could be wrong but that is my understanding anyway. The different bases are still kind of foreign to me.