Weeping

Yes, taking it out is a great idea. Since your going to have to drain it anyways. Take a quick picture of the linkage - take the clips off each end of the linkage and remove them, take your shifter boot off, two bolts and your shifter comes off. Now the easy part- take the four 3/8's bolts off the driveline and remove, this would be application specific but I loosen my exhaust from my headers so I can put a jack under the transmission and when I take the 4 cross member bolts out I can lower the transmission down and tilt the motor back a little bit to gain access to the last four bolts holdingthe transmission to the bellhousing. I put a scissor jack under the bell housing to keep the motor from flopping back too far and hitting the distributor against the firewall and also I like a scissor jack because it won't lose fluid or anything over time. And I put my hydraulic jack under the transmission once those 4 bolts to the bell housing are out and the 4 bolts to the crossmember and wham-o its in your hands. This is a great time to check and reseal everything and even book your linkage and shifter back up and make sure everything is all correct. You can check all the washers and lubricate the shifter and all of the little grommets in between the shifter linkage. You couldn't really improve your experience with the transmissions performance but having nice tight linkage.
edit: I almost forgot you'll have to unplug the reverse light and undo the speedo cable
I don't have that stuff in my car