RE: "most tub drains go through the wall rather than down through the floor" - I've never seen a tub connection through the wall. Tub connections begin below the tub drain, below floor level.

Are you going to keep your current shower or replace it with the tub? Replacement is the easier option, IMO.

Most DIY books at the home centers will show how to do the following:

To connect the tub to the existing shower drain, you would remove the shower and break the concrete up around the shower drain, exposing the piping. Also break up the concrete over to where the tub drain plumbing will be. The plumbing below the slab is probably plastic piping, assuming the house isn't old. The old shower piping is cut off and new plastic fittings are glued on to bring the drain over to the tub. Be sure to slope the drain piping at 1/4" drop per foot of run so things drain properly. The shower drain should have been vented, so chances are you're drain venting is OK. The exposed piping can be covered with a bag of quickcrete, but leave an area around the tub drain connections exposed, maybe 12"x12" around the trap fitting. After the tub is in place, you come in through an access opening in the wall at the end of the tub and connect the drain piping to the tub. Obviously, you can't do this if the tub is placed against an outside wall, so you might have to switch the tub orientation to get the drain where you can get access to it.

This isn't outside the abilities of a DIYer. Just study, think, and plan and you should be able to do the job.

I don't think i would want your contractor doing any plumbing work for me if he thinks the tub drain goes through the wall.

The pipe that connects to the back of the tub overflow makes a 90deg turn and runs straight down. The tub drain tee's into that line and it continues straight down to the P-trap all of which is under the tub, but what do i know, i am only a plumber.

Can the tub be raised off the floor and the drain run across the floor into a floor drain?

I've been researching this for my own basement and thought it'd be good to respond on the thread. There are tubs that are designed to connect above grade (if you can't break your slab, for example). They have the plumbing and bottom of the tub raised a few inches, so you sacrifice water depth or stepover height for ease of installation. Kohler is the brand I came across first that listed this feature on their website. This would allow connection to an in-wall stub-out or existing shower drain stub nearby assuming there was an appropriate trap in the slab already.