I dont think swapping litters will make any difference, its nature , you cant alter there basic make up , i dont think its anything to do with the jill being domesticated if you swap over
Apart from anything else you will need to hang on to the offsprings for christ knows how long before making any decision on what stays & what goes , moving on unsuitable animals will be hard , but full hybrids it will be almost impossible , who wants stock they cant handle & are basically as much use as a chocolate fireguard