As others have said, there a various strategies for reducing the numbers of people you see along the way, including choice of route, choice of daily stopping points, time of walking. That said, your concern seems to be the end of the trip.
More broadly speaking, the St. James Day crowds should be pretty much gone from Santiago (and the earlier stops in Galicia) if you are arriving in August. You'll still have to deal with the summer crowds and the Holy Year crowds, but not the St. James Day crowds. The summer crowds aren't too bad before the last 100km. Actually, May and September seem to be the busiest times of year for that portion of the route. But it is different for the last 100km, when the summer is busiest. That's where C Clearly's suggestion of the Invierno comes in really handy or, failing that, PerpetualPilgrim's suggestion of staying outside the regular stops that all the groups will be using. Which leaves you with Santiago itself. If crowds are a concern, you'll probably want to consider the timing of when you do things: when you visit the Plaza del Obradoiro or which mass you go to in the Cathedral, etc.