The end result

Lie down. If you sit up, you get pelvic pressure and may deliver early.
Sit up. If you lie down, you get reflux.
Lie down. If you sit up, you get morning sickness.
Drink milk. It fights the reflux.
Don't drink milk. It makes the morning sickness worse.
Drink ginger ale. It fights the morning sickness.
Don't drink ginger ale. It's too acidic and aggravates the reflux.
Drink peppermint tea. It soothes the stomach.
Don't drink tea. It doesn't mix well with stomach acid.
Eat breads. It absorbs some of the stomach acid.
Eat nothing, or you'll throw up from the morning sickness.
Eat anything you can so you don't lose more weight in the pregnancy.

I have discovered that it doesn't matter whether I sit up, lie down, eat, drink milk, drink tea, drink ginger ale, or do anything else ... the end result is that I will throw up regardless. And that's just a lovely thing.