Rich, the air purging will only succeed if the transmission is full of oil throughout the process. Tuff Torq says it may take up to 2.2 litres of oil. Item 7 of this page describes the purging:
http://www.mytractorforum.com/showthread.php?t=161413

Note the reference to it taking up to 10 minutes of purging at idle before you lower the wheels to the ground.

The symptoms you describe sound as if there is air in the hydraulic circuit. There are several things that could cause this - in particular, aerated oil at the end of the purging process. Because the L110 does not have a proper oil reservoir, de-aeration of the oil may be a protracted process. FWIW, my approach would be to let the machine idle with the rear wheels elevated while alternating between forward and reverse, until I had clear oil in the filler: no signs of aeration. It is usually recommended that you switch the motor bypass valve on and off (i.e. operate the transit lever) a number of times while you are doing this. Of course some topping up along the way is likely to be required, due to the L110 not having a reservoir.

Please do not run the machine above idle, or lower the wheels to the ground, until you have all of the air out. The howl you described is a cavitation sound, and it is accompanied by cavitation damage to the pump and motor.

If it makes you feel any better, you are not the first person to go through this personally-unsettling process. You may find this description hauntingly familiar:
http://dir.groups.yahoo.com/group/John_Deere_L100_Club/message/1473

Just imagine how much easier this would be if JD had bought the optional oil reservoir and transmission drain plugs:
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