I gotta congratulate you for taking on the toughest job on your washer. The transmission replacement is daunting if you've never done one before.
OK... about your question.
Here's a place with detailed instructions
(and pictures) on how to do the 2X4 trick. If after doing that you still can't get it, then try tapping (actually a little more
than just "tapping") the agitator with a rubber mallet. This will (hopefully) loosen any rust on the splined shaft allowing the 2X4 to do its' job.
As a last resort, you can get yourself an "Agi-Tamer
". It's a tool that we in the appliance repair biz use for just this problem. It's a snazzy little gizmo that fits between the bottom of the agitator and the tub. It has a water hose connected to it... you then take that hose and put it on the cold water valve behind the washer. Then you slowly open the valve filling the Agi-Tamer with water. As it fills, it expands and forces the agitator to lift with it. You have to be careful, though. I've seen agitators fly off the shaft like a cork from a champagne bottle! So if you go this route, put your 2X4 over the agitator as the Agi-Tamer fills to keep it from flying, OK?
(*NOTE* ---> the link to the Agi-Tamer above shows one designed to use air pressure, not water (like the one I use). I've never used one with air, but it appears that it'll hook up to a bicycle tire pump or one of those inflatable swimming pool toy electric pumps. Just a word of caution here... knowing what I do about Hydraulics and Pneumatics, the pneumatic model WILL MOST DEFINITELY BLOW THE AGITATOR OFF THE SHAFT!!! So, take care if you use that model, OK?
Now where to get one. This is a specialty tool sold to appliance repair guys (and girls... although I've never HEARD
of an appliance repair girl). You may try calling a local appliance parts retailer and see if they have one in stock or look around on the web. They run about $50, so it's kinda pricey to buy it only to be using it once... why not call an appliance repair company and explain what you're trying to do. Ask them if any of their technicians carry an Agi-Tamer on board their sevice vans. Then maybe work out a deal to rent it or borrow it. Or you may simply schedule one of their technicians to come over and remove the agitator FOR
you. <--- That's probably the way to go, btw. Using an Agi-Tamer is kinda
dangerous and a reputable company might not want to take on the liability of you using one of theirs just in case you poke your eye out or something.
So there ya go, KR! I hope this solution was satisfactory for you and that it helps you get that pesky agitator off. If it did, please remember to rate me as "it solved my problem", deal?