At this point seeing all the severe damage... I personally would go to a local appliance repair shop and see if they had an Old Maytag transmission lying around and replace the upper half of the transmission. I always had 3 or more sitting complete un-rebuilt units around when working in the shop. It is best to look in the yellow pages and find some fella close by that sells USED washing machines. (check classifide ads, penny saver and the local dump recycling centers also) He may even sell you the whole transmission. Even if he has the new style that looks like a differential you can use that one also. I would not return the one your working on to service without replacing the agitator shaft and upper transmission cover.
Transmission PN your looking for is PN 2-3438 I hate using another competitors link but here: http://www.appliancepartspros.com/09-transmission-parts-for-maytag-a612.html
Any brand new transmission is the orbital type unless you can find a source with New Old Stock NOS. New transmission type is PN W10172457
Additionally... seeing this much water damage the radial bearing in the brake assy in the base of the unit is also probably no good. The brake has a set screw on the upper side of the base that must be removed before turning the brake with a strap wrench even though their is another special tool spanner that your supposed to use in the shape of a C with 2 plates that fit top and bottom of the brake housing grasping 2 of the brake screws to turn it.
Radial Bearing is PN 200835
Looks like your in a worst case scenario here... Personally if the base and tub(s) are in good shape I would try to find the parts to fix this unit as it will give you another 20 years of service with lite to med, usage.