That gold tub is definitely a Kohler Villager -- can't miss that Nike swoosh on the apron...
The complicating factor here is that finned copper radiator pipe buried inside the apron--a clever way of hiding the radiator in the room.
I'd say that the first thing you need to do is remove the finned copper piping. Are there removable fittings where the pipes meet the floor/walls? Or did they solder it in?
If you can't get at those fittings (or if they don't exist), then I'd say you have no option other than to continue breaking the tub into pieces. Then (at least temporarily) remove the radiator pipes before you put a new tub in. The toilet is going to have to come out, and it would probably make it easier (more room to maneuver) if the vanity came out too.