Benders 1, welcome to the forum.The OLT can be done very quickly, 7 hours and 25 minutes.
http://fastestknowntime.proboards.com/t ... k-tasmaniaSo it's really a day trip. Not a day walk, a trip.
While it should be possible to do the OLT at a more leisurely pace in four days, I'm not persuaded that this is a good idea. Part of the charm of places like Cradle is that the pace is slower. Take in the scenery, and most certainly do side trip. I'm aware of two parties next summer that are taking 10-12 days, with many side-trip - Cradle, barn Bluff, Pelions, Ossa, out of Pine Valley.
The other factor is the weather. If it gets bad than progress will be slow, and there may be the need for a rest day. Take a tent and treat each hut as a bonus.
Are you intending to end at Cynthia Bay, or not do the entire OLT and end at Narcussus? Also, why do the walk in four days? if you want a booking this summer best move, places are filling fast and many days are full.