Necro but I just pulled the rear motor mount out on my '04. That was a bear. Tried for about 2 hours last night and decided to give it one more go this morning...
You *must* remove the air intake and battery and relocate the cruise control module up and to the left. I also unbolted the cruise control module bracket and moved it down to the right. There is no clear path for removal otherwise. Take a bunch of pictures as you peel it apart to make it easier to reassemble. I then found all my mount bolts and soaked them in kroil after removing the intake. I let it soak overnight and reapplied when I started removing the mounts.
For reference, this video is very, very helpful:
https://youtu.be/B-EyHZkw0Dk?si=KeMMK9FZVd2jc8XB
I used the spare tire jack and the rubber pad for my floor jack to lift the transmission - I was inspired by the guy in the video. I jacked up the transmission where it bolts to the engine, not under the transmission pan.
For starters, get some upward tension on the transmission; don't go nuts but maybe 3 turns on the tire jack once it's butted up against the transmission. Get a 17mm impact socket and a long extension; the longer the better. Look in through the driver's side wheel well and you'll plainly see the bolt that attaches the mount to the motor bracket. If you're using a breaker bar you will probably need a 2 foot long extension; I personally used a small impact driver and a 10 inch extension; it barely all fit. Break that bolt loose, reach in and fish it out once it's free.
There are 3 nuts and 1 bolt in the subframe beneath the mount; the video I linked above shows where those all are. I personally used a 14 mm impact rated deep socket and a small impact gun to remove them all. I'd imagine that a breaker bar will work just fine. If you're working on the ground I hope you're not claustrophobic for this part

After 20 years they were pretty filthy.
NOW COMES THE FUN PART; congrats you just did all the easy stuff.
Next I removed all the 14mm mounting bolts connected to the frame from the driver's side motor mount; it will rest in place if you leave the mount connected to the motor. I used an impact where I could, a breaker where I could and lots of penetrant. The back rear frame bolt on the driver's side mount seemed like it was going to round... thankfully it didn't. I advise a long 6 point box end wrench for that particular bolt; I only had a 12 point and was lucky it didn't round out. I hit it with more kroil and waited another 10 minutes before trying a second time.
I then removed the nuts from the front motor mount, also 14 mm. These can be accessed under the front of the car.
Now the motor is mostly free (minus the passenger side mount) and can be moved up and down with the tire jack. This is also a great time to replace the driver's side lower control arm (going to do that tonight).
Watch this portion of my linked video until the author gets the mount free:
https://youtu.be/B-EyHZkw0Dk?si=KeMMK9FZVd2jc8XB&t=488
He mentions that he started with the motor high up, freed the mount and then lowered the motor down. I did the same. I got the long stud free from the subframe but was having a very hard time rotating the mount out from the bracket. I gave up last night and lowered the motor so that it didn't strain the CV axles overnight.
This morning I decided to take one more crack at it. With the motor lowered but the mount still free I was able to tilt the top of the mount almost all the way back to the engine (you see it in the video). I then rotated the whole mount clockwise while pulling up on it. It took a significant amount of force but I was eventually able to work it free and then pull it through the rats nest.
I still have to reinstall it!! I've heard that's even more fun... I started with the rear mount first as I've heard it's best to leave the other mounts for later since busted mounts have extra play in them.