It might help if you change your thinking about what the pilgrimage is, or isn't, for you. For a start, every pilgrimage is a complete thing within itself, whether you walk for five days or fifty. Even if you might think that one day you might walk all the way from SJPP, Lisbon or somewhere else, if you walk a section now, that will be your pilgrimage.
Unless you have a definite plan to complete a particular route in sections, which I think is a perfectly good way of doing some of the longer routes, I would be inclined to think that ending in Santiago would be a better option. There is something very special about arriving there at the end of your pilgrimage that you can take away that I don't think you would get stopping somewhere else.
Splitting the camino over two or more discrete sections is clearly an option. When my wife got ill when we did the CF together, we in effect were forced into doing that. I wouldn't do it voluntarily myself. It was too disruptive of the flow of the camino for me, even though that is what we did to make it work. We saw others doing something similar, such as crossing the Pyrenees, and then taking the train or a bus to Sarria and continuing from there. Some were walking several sections, including from Sarria. That seems rather artificial to me, trying to pick the good or interesting towns to visit. It seemed more like a sight-seeing walk than a pilgrimage.
My last point is to echo the suggestion that you consider the Camino Portuguese route, starting at Porto. I have walked several different routes now, including the Central route from Porto. It seems to me that for someone doing their first Pilgrimage to Santiago de Compostela, it has the same advantages as were lauded of the Frances in terms of places to stay, the numbers of other pilgrims walking, etc, but doesn't have the same crowding after Tui that seems to be occurring on the the Frances. You would still need to determine which of the routes to use leaving Porto, but it appears to me that none of them would present any particular difficulty if you plan to do sensible distances.