I'm with 1fatcat (and bonnevillain) on this one. When your engine is quite hot the Pressure Control Selanoid (or EPC as referred to below) will mis-read how much pressure to apply and causes hard shifts especially in the first couple of gears. Next time it happens, pull over and turn off your engine for 20-30 seconds.
If the hard shift goes away for a while then it's connected to the PCS. You can replace the PCS, or perhaps first try what worked for me. My hard shift problem went away as soon as I installed a 180 t-stat, keeping everything just cool enough to avoid the PSC issue. The hard shift, which I used to experience almost weekly, has since happened only once in about a year and half (and when I drove it REALLY hard on a REALLY hot day).
from the link bonnevillain offered:
"Intermittant Harsh Shifting / Pump whining, Possible Code P1811:
This is perhaps one of the most common problems with this transmission. It has been a problem since the release in 1997 and can happen for no reason at all even with clean fluid and very low mileage. The EPC solenoid is probably bad and again is very common to happen. The EPC solenoid controls line pressure and has a spool valve which oscillates back and forth to regulate transmission line pressure based on commanded pcm signals dependant on lots of various inputs of the vehicle. The spool valve in the solenoid will bind up and cause loss of pressure control from the pcm. The pcm constantly monitors shift timing in milliseconds and if this is not within programmed parameters after a few shift cycles the pcm triggers trouble code P1811 which is Max Adapt / Long Shift. This code will not set the SES light but will dissable all adaptive shifts and will max out line pressure in the transmission which causes the harsh shifts and can also cause the transmission pump to whine because it is supplying fluid at a high rate and pressure and puts more stress on it thus creating the whine.
Generally shutting off the car will make this condition go away until you drive a few more miles or the vehicle warms up and the harsh shifting will return. Replacing the EPC solenoid will most likely correct this condition and again is probably the most common problem found in any year of this trans. I will also add that a worn out transmission can cause this. If the fluid looks bad, dark, and smells burnt or lots of fine dark sludgde or a dark film of material is in the bottom of the pan then there is probably internal damage. Once clutches become burnt and have excessive wear shift timing will be greatly extended and the pcm will fall outside of its set parameters and code P1811 will turn on, again commanding higher line pressure and harsh shifts but an overhaul in this instance is the only proper fix."
The thud you experince when moving from park to drive/reverse may still be a bad trans mount. They don't necessarily "look" busted, but the "engine jump" test as described here is your best way to test the mount.
Pic of mount torn underneath out of sight:
http://i415.photobucket.com/albums/pp23 ... 0_5321.jpg
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Mark
The Familyman's Trans-AmIntense 3.4 MPS, Intense FWI, Intense PCM, copper NGKs TR55's, MSD wires, MSD coils, BWD ICM, MagnaFlow High Flow Cat, drilled 180 'stat, solid front mount, Monroe Max Air rear shocks, Moog rear mounts, Moog suspension bushings, cleared front corners, 190,000 miles