Yes, I think that is pretty much what I meant.
Have you played with the Chicken Calculator at all?
http://kippenjungle.nl/chickencalculator.html
You can change the genes in the dropdown boxes, and the picture of the chicken will change. It can also predict results from crossing the chickens, but I don't use that feature as much.
The default genes in each box are marked with +
This means they are the wild-type genes, found in the original wild junglefowl ancestors of chickens.
Those default settings are pretty much the ones that a Welsummer would have.
For White Leghorns, the first box changes to E/E
That is "Extended Black," which spreads black all over the chicken.
And White Leghorns have I/I instead of i+/i+
That is Dominant White, which changes black to white (I think the "I" is because it "inhibits" black.)
Because E and I are both dominant genes, the first generation of crossed chicks will show both of those traits (black all over, with the black turned to white.)
The next generation is when you get chicks of types 1,2,3,4 in the chart you drew. 1 is chicks who inherited both E and I, 2 have E with i+, 3 have e+ with i+, and 4 have e+ with I (the combination you want.)
There are some other genes that White Leghorns usually have that are different than Welsummers, but the main ones should be eliminated if you start with a Welsummer rooster and a White Leghorn hen, then use just the daughters from that cross to breed with more Welsummers.
That is because of how the sex chromosomes work in birds: Males have ZZ, with one Z inherited from each parent and one Z given to each chick. Females have ZW, with Z inherited from the father and given to each son, while W is inherited from the mother and given to each daughter.
Among the known genes on the Z sex chromosome, the Welsummers have all the ones you want. The mixed daughters inherit a Z chromosome from their Welsummer father and a W chromosome from their Leghorn mother, so the only Z chromosome they have is the one you want (the one that originated with the Welsummer rooster.)