Also, I don't follow what's going on. You say you're cooking it over a pan, but the smoke happens when the grease hits the bottom of the oven. Is it missing the pan? Is the pan overflowing?
Sorry, I'm good at making things confusing. Those are two different instances. Sometimes stuff makes its way to the bottom of the oven and that causes smoke, but when cooking bacon it also causes smoke.
Maybe try cleaning the oven? My thought being that there might be a coating of grease on the oven and it can't take any more. Yeah, okay; it doesn't really make sense, but it's something to try.
Yeah, I had the same thought, but I've run the oven through two cleaning cycles now, and it's been professionally cleaned

Alternatively, you can try a
roasting pan. This will prevent the grease from the food from dripping onto the bottom of your oven, effectively solving your problem. As you can see, it's not an expensive solution either. I'm using one of those things and I like it very much. It's easy to clean and very handy to use.
Yeah, I've been meaning to get one of our own. We used my mother's for the turkey on Thanksgiving... It might be worth a try.
Just do what I did and get rid of the smoke detectors.
Haha, good idea

Actually, we've already been doing the less-than-ideal thing of covering them with Ziploc baggies whenever we know the oven is going to do this. (we take them off afterward)
Also, I have a fan in the kitchen window aiming out, so while the kitchen gets smoky, the rest of the house is ok.
Sadly our kitchen window doesn't open. We'd have to keep a door open, but we have cats that we don't want to escape.