Do they make tub drains that go straight down from the drain instead of the overflow?

I roughed in the drain for my tub to where the drain will be, rather than where the overflow pipe would be. I know they make the drains you push down that go straight down from the tub drain, but do they make the kind with the lever and overflow that go straight down from the tub drain rather than from the overflow drain? Also, if I were to use one of the push down style drains, are the overflow covers water tight?

Yes. Check these catalogs:

http://www.macristyindustries.com/csbcatalog.shtml

http://www.watcomfg.com/WATCO/Downloads/WATCOPriceGuide.pdf

drain

Doing it the way you did it means that the drain has to be EXACTLY in the correct position. There are several companies making toe outlet drains. One that is being advertised now has a flexible green hose from the overflow to the tee with a cable operated pop up. I am not sure if it is a Gerberit, or someone else's.