Generating points uniformly distributed over the SURFACE of a standard simplex
I created an algorithm for that. for detail see 
    http://www.sciencedirect.com/science/article/pii/0098300493900457

briefly speaking, you can use following recursive formula to generate:

x_1=1-R_1^{1/n-1}
x_k=(1-\sum_{i=1}^{k} x_i)(1-R_k^{1/n-k}),    k=2,…,n-1
x_n=1-\sum_{i=1}^{n-1} x_i


Best wishes