First of all, my condolences. Three centipedes a day is enough to test anyone's sanity, especially if they're big ones. You may very well be right about last night's centipede getting ready to lay eggs; this is the right time of year for it. Spring (and fall) is also when centipedes are most active, and you're likely to see them most often.
Honestly, centipedes are tricky to get rid of. The only household products you can use to kill them are boric acid and diatomaceous earth. They may not be "household products" in the sense that you already have them on hand, but you should be able to find one or both at a home supply or hardware store, and they are environmentally/pet friendly. The instructions for both involve applying them along the edge of your foundation and in any indoor/outdoor cracks and crevices where centipedes may try to hide or enter your home. If a centipede comes in contact with either product, it will die. Unfortunately, products designed to eliminate infestations all at once, like insecticide fogs, don't work well on centipedes.
You can also deter centipedes by keeping your house as dry as possible. Use dehumidifiers or air conditioning if you don't already, and if you have carpet, try sprinkling an odor removing powder (Arm & Hammer makes some good ones) before you vacuum. I find that this draws moisture out of the carpet, and I usually have a slowdown in my centipede sightings for at least a few days afterward.
Good luck.