In that black sex link cross, the father would be the Dark Cornish and the mother would be the Barred Rock. Cornish are not known to be great egg layers but since that is the rooster, who cares. Roosters don’t lay eggs. Barred Rock hens normally lay pretty well, especially BR from hatcheries. So you should get plenty of hatching eggs from those parents.
The male offspring from that cross should make really nice meat birds with large breasts compared to most dual purpose crosses. My one concern is that the dark feathers will show up if you pluck the carcass instead of skin it. Whenever you pluck you leave pin feathers behind. Light colored feathers like white or buff don’t show up that well so you get a prettier carcass with them compared to a dark red or black bird. As far as a meat bird cross that should do well.
The concern does come in with the pullets from that cross. With any dual purpose cross the pullets should be bigger than leghorns or the commercial hybrid egg layers. That means they are not going to be as efficient at turning what they eat into eggs since they have to eat more to maintain that big body. The Cornish (also called Indian Game) are bigger than most dual purpose birds so this could be a problem.
Also since Cornish are not known to be great egg layers the pullets will probably inherit some of those tendencies from their fathers. The rooster contributes just as much to egg laying genetically as the hen. Hatchery birds tend to lay better than the breed norms, so the pullets from this cross may not be terrible at laying eggs but that’s questionable.
Also hatchery birds are not normally as big as breed standards either. Breed just doesn’t mean as much with hatchery birds as it does with someone that is breeding to breed standards. You may not have done as well for meat or as poorly for eggs as you think. It’s really hard to say with hatchery birds. That makes it hard to make recommendations based on hatchery birds.
Before the advent of the Cornish Cross, Cornish X, hybrid broilers (whatever you want to call them) in the 1950’s the standard commercial meat birds were New Hampshire, Delaware, and some flocks of White Rocks. Since then hatcheries or much of anyone else have not been breeding to meat standards so a lot of the qualities that made them such great meat birds have been lost. There just isn’t that much difference in today’s hatchery New Hampshire, Delaware, and White Rock and any other hatchery dual purpose breed.
Most breeders for these breeds are breeding for show. If you get your birds from them they will be bigger (and a lot more expensive than hatchery birds) but most are not breeding for all the traits that made them great meat birds to start with, plus they are probably not breeding for good egg laying either. You also get the bigger bodies so they are not as efficient as turning feed into eggs as many smaller birds. There are a very few people that do breed for production but most people breeding for show are mostly breeding for what the judge sees and the judge does not see how fast a cockerel puts on weight or how many eggs a pullet lays. There are no magic chickens out there. They all come with some qualifications.
The quality of the stock you get will have a huge influence on the quality of the offspring, but if I were following your goals I’d look hard at a New Hampshire male over a Delaware female. You should get a reasonable dual purpose carcass from the males but they will not have the bigger breasts you might get from a Cornish. The pullets should lay really well. The offspring will be red sex links, very easy to tell apart at hatch. The males will be mostly white so you should get a pretty carcass if you pluck.
With hatchery quality stock I don’t know that these will be that much better than most other dual purpose crosses, but I think it’s a reasonable approach. Good luck!