Sounds a little bit like a bearing; a rhythmic squeak that increases frequency as the spin winds up. Is this the spin brake slipping? Once up to speed, the squeak stops, so it is not likely a bearing.
Should I oil the brake package? If so, with what? Nobody around here stocks Maytag tranny oil.
There is no squeaking or grinding at the end of the spin, as reported in other posts on this site.
Post# 549841 , Reply# 1   10/16/2011 at 17:06 (4,547 days old) by arbilab(Ft Worth TX (Ridglea))  
Least daunting to fix is if the belt has a slick spot on it. It would squeak at the rate the belt went around and stop at speed when the torque load goes down. Also confirm the motor slides are clean and free.
I haven't had a Maytag apart beyond that, was never necessary.