FYI: I just tried with some fresh alkalines, but still the same behavior.
@Alex: You said you cleaned the battery contacts. Just those in the Battery holders, or the ones in the grip as well? (I don't want to risk killing the grip by flooding it with contact spray).
Also, maybe an other SQ-Ai owner can confirm that this is normal: when i use the manual winding crank, after shooting there is a bit more force needed from about 120° to 240° and even some more until 300-330. i.e. the needed winding force isn't constant for the whole 360° degree turn.