I find it useful to start with the last point and add priors, at each step visualizing a bounding area. It's usually helpful to consider at least 2 points ahead, because to cross between two existing points requires taking a shorter hop to the vicinity of the mid-point between them, but is worthwhile on the next hop. For seven points I get (excluding fudge factors to force choices):
¼√3,¼
0,½
0,1
½√3,½
1,0
1,1
0,0
total distance 4.93185
For eight points use the same sequence with the addition of ¼√3,¾ at the beginning, giving
¼√3,¾
¼√3,¼
0,½
0,1
½√3,½
1,0
1,1
0,0
total distance 5.43185
A ninth point would go where the bisector of (1,1)~(¼√3,¾) intersects (0,1)~(1,1), approximately 1,0.666 .
