I read through the answers and believe one thing needs to be said re: your “feasibility study”. It is physically possible, therefore “feasible” depends entirely on your level of technology. You are essentially asking if we can sink all seven pool balls & the eight ball in sequence with one shot. Yes, with perfect information, it is possible.
To make this feasible you need:
Extremely precise location and momentum information on every rock in the solar system (not just the ones you are using, because everything has gravity).
Enough time to “hit the cue ball” ( I’veIOW the first rock)
Enough time for all the other rocks to get into position and move each other (completely random number)
Extremely precise location and momentum information for the rogue planet.
Enough time for this scheme to intercept the planet before it is too late.
The ballpark range for having all this I formationinformation, for I guessforming the plan, then launching the chain reaction will be between hundreds of years (in a perfect scenario) to millions of years (only limited by the time you get perfect information about your planet.)