How would I "stabilize" the "incomplete Quail?
What would the easiest color to get them to breed true as be? That is a very confusing sentence, sorry.
The thing with 'incomplete' patterns is that they often come from heterozygous gene pairs. Basically because they are from a mix of patterns and may only have one 'correct' gene out of each possible plumage gene pair that would make up a specific pattern. In this case rather than having Co/Co and Ml/Ml to make a quail pattern, they might have Co/co+ and Ml/ml+, as an example. When you then breed birds with incomplete patterns, they might pass some of the correct genes and some of the incorrect genes on, with a huge number of different combinations possible. So, in the example I gave with Co/co+ and Ml/ml+, the offspring could be Co/co+ Ml/ml+ like the parents, but they could also be Co/Co Ml/Ml, Co/co+ Ml/Ml, co+/co+ Ml/Ml, Co/Co Ml/ml+, Co/Co ml+/ml+, Co/co+ ml+/ml+, co+/co+ Ml/ml+, or co+co+ ml+/ml+. As you can see, that's far from breeding true--and I only considered two genes here, not the numerous others that might be at play! A lot of these pairings would look similar to your birds because of the dominance of the genes, but you would still have the issue of them not breeding true for future generations. I think if you want a pattern similar to those birds that does breed true, your best bet is to just go for quail patterning.
As for blending in, it really depends on your environmental conditions, like U_Stormcrow pointed out. There's always the classic wildtype partridge (the pattern that Light Brown Leghorns have, for example) as the standby for a color that blends in well, though. It worked for camouflage for wild junglefowl after all!