You probably won't be able to get viable hybrids between the Persian Carpets and the others, but don't let me stop you from trying. If bi-colors and tricolors interest you, try the Whirligigs. Some Whirligig strains have "run out" to mostly single flowers, while other strains still have a good percentage of fully double flowers. Both kinds are worth growing, and full of surprises, including a few mutants.
"That's true, but I like the "cheerful" look of orange, yellow and gold. "Scarlet" would be cool, or multi-colors..."
There are several shades of red in the scabiosa flowered strains, including scarlet. The Whirligigs that I mentioned have many multicolor combinations, and I have crossed them with other zinnias, including scabiosa types.
"...but then I would have to create new traits that were not present in the F1s, which I think would be much harder."
Actually, that can be easier than you might think. For example, the "shaggy dog" flower form that I led off with here wasn't present in any of the parents or grandparents of that specimen. It arose as a unique new recombination of genes from the genes that were provided by the parents and grandparents.
The zinnia chromosomes contain a lot of genes, and the mathematical number of ways that they can be recombined is way beyond astronomical. Many of those recombinations are very similar and produce zinnias that differ only subtly from each other. But some of those recombinations can produce improbable and very unique new zinnia forms.
Growing seeds from hybrids, or crossing hybrids with each other, is something like pulling the lever on a giant slot machine that has very many different wheels instead of just a few. If you are willing to grow a lot of recombinations that result in culls and rejects, you stand a chance of "hitting a few jackpots" and getting a few specimens that are new and good and different from any of their ancestors. Zinnia breeding is a game of chance.
People usually say that you shouldn't save seeds from F1 hybrids, because the results are so unpredictable. They are unpredictable because recombinations can occur in many, many different ways. Save seeds from F1 hybrids because they are unpredictable and full of surprises.
A recent sort-of-scarlet scabiosa flowered zinnia is pictured.