To make your crossbreeding system as easy as possible colour tagging is a good option. You simply use 3 different colour ear tags on the calves. Calves that need to be sired by Holstein get, for example, a blue tag. Calves that will be sired by Swedish Red get a red tag and the calves that will be sired by Montbéliarde get a yellow tag. When you see a blue tag you know that that animal will be inseminated with Holstein semen etc. When you have your 3rd generation ProCROSS calf, you can use the blue-tag again. Inbreeding is a non issue anymore.
In the image on your right you see a cow with a red ear tag. She has to be inseminated by a Swedish Red bull. Instead of a seperate tag, you can use identification tags that can be installed behind the normal ear tag.