<reply to headintheclouds>
I presume we're both talking about a stall speed reduction, from the "clean" (no flaps / slats / blowing / suction / doovers) value, to 60% of that speed - for example, a reduction from 60 kts clean to 36 kts in landing configuration?
Without splitting further hairs, such an aeroplane could not be made certifiable under LSA; would not have much utility within the LSA weight limits; does not comply with the LSA "simple aeroplane" concept; and would require a lot of engineering, development, and money to achieve.
A solution to the very low stall speed aircraft exists, however - they're called "gyrocopters".
The painful reality Dafydd keeps alluding to, is that any certifiable aeroplane optimised for ton-miles per dollar-hour will find it's flap power to be limited by pitch control authority. There is one known "improvement" to be had (in this respect) over the single-slotted hinged flap, which is the Fowler; by the NACA data as plotted in A&vD, a lift coefficient of up to 2.8 (2D) can be had with about half the pitching moment increment of simple hinged flaps.
The Fowler has the additional benefit that, when the deflection is increased, the Clmax decreases slightly, and the drag goes up markedly. This means that one can use them as landing flaps in the high-drag position, and - if a balked landing becomes necessary - dumping a notch of flap both reduces drag and increases the available lift. I suspect that this is now considered too complex for a "pilot of average abilities"...
The downside of the Fowler is the mechanism required to push the flap 0.3c (or whatever) rearwards... especially as the cable interconnect used by Cessna is now frowned upon by design standards*.
*Certifying Authorities actually; as the flap interconnect is also the flap drive, and is a complex system with a bunch of single failure modes resulting in catastrophic accident conditions...Since I have yet to see any recreational aeroplane with a properly-shaped flap shroud - despite the data having been in the public domain for the last 80 years - I have to conclude that most LSA designers aren't serious about keeping stall speeds down.