Just picked up on this thread. IO540 is quite right that lifting the nose wheel early in 'sticky' conditions reduces wheel drag. This is not only by not ploughing a furrow through the mire with the nose wheel, but even early in the run, some lift will be obtained from the increased AoA, reducing the drag of the mains.
I learnt on a grass strip in a C150, and on my 4th or 5th solo take off, it got to about 30kts, when it would go no faster ploughing through the mud. Feeling that I could drive it like that to end of the strip, instinct caused me to jerk the stick back momentarily, which lifted me an inch or so to be aquaplaning on top of the mud, when I then accelerated normally to lift off.
A word of warning. Even on a hard runway, lifting the nose early also increases drag from the increased AoA and angled fuselage, so acceleration will be slower, and take off run greater. As IO says, this can be much better than the even more reduced acceleration caused by ploughing through mud.
However risks are that you will get off early in ground effect, without enough power to go anywhere whilst on the back side of the drag curve (not much likelihood in a TB20!), or the oncoming hedge at the end causes you to pull back even further, which prevents you getting airborne at all. AAIB reports have both of these cases. Several years ago, an aircraft trying to depart Bodmin lifted its nose early, finished up scraping its tail on the ground, failing to get off as it went into the hedge.
Muddy strips almost preclude confidence in take off run calculations, especially as its going to be different at various point along the strip.
MikeJ