OK, it sounds to me like you've got a line pressure problem, and it only engages when you rev up the engine (which should increase your line pressure if it's below target). But it makes no sense to me that it can be blatantly slipping and not set a Gear Ratio Error fault.
I would recommend:
1. Check the fluid level, idling in PARK. Do not put it into gear any more, if you can avoid it (you are frying your clutches when you do).
2. If fluid level is OK, drop the oil pan and check the filters. Make sure they're not loose / cracked / dislodged / etc. Check the side seam on the main sump filter; sometimes they split open along the seam.
3. If filters are OK, check for any parts or chunks of debris in the pan.
4. If pan is clean and all looks good, button it back up and refill (should take about 7 quarts). Then find your transmission relay (should be in with the fuses, etc.). Disconnect the trans relay, then start it up and try Drive and Reverse. It will be in limp-in, so you should get a harsher engagement than normal. Don't try to drive it, just see if the engagements are any different. If the engagements now seem OK, then you probably have a wiring problem (line pressure control solenoid circuit shorted to ground). If the engagements are unchanged (still mush), then you probably have a stuck main regulator valve, which is inside the pump and requires trans removal to fix.