Your description of having to give it tons o' throttle to get moving sounds like worn clutches or a slipping torque converter.
How'* the transmission fluid look? Smear some from the dipstick onto a white rag...is it nice and red and "sweet" smelling, or sorta brownish and burnt-smelling? Any little black particles?
Perhaps do a stall test: parking brake on, left foot holding the brake pedal down firmly; put it in Drive, and press the accelerator quickly just
until you hear a "groan" or "creak" from the tranny and note the rpm'* on the tach...then let off the gas (and put it back in Park). You should be reading around 1800-2000 rpm on that test. Significantly higher and you're TC may be shot.
(Note: Stall testing like this can be VERY hard on the TC...do it quickly, and only once