If you don't want to overkill these projects, to the best of my knowledge, the # of hammers required to finish the project is equal to the # of hammers needed for the 2nd place prize X the # of civs left* in the game. Therefore, half of that +1 (or the # of hammers needed for the 3rd place prize X the # of civs left* in the game) would be what you need to guarantee 1st place and you can then switch your production back to units/building/wonders. As has been said before, you can hover the mouse over the build icon on the main map for any city that is producing the project to see how much your civ has contributed.
*I'm pretty sure it's the # of civs in the game when the project begins and will not go down if someone gets eliminated before it's completed, but I'm not 100% certain.