Stacked LFSR - why not used?
Your design seems to be a byte-wise generalization of Jennings' multiplexed generator rather than the alternating step generator. 

S. M. Jennings, “Multiplexed Sequences: Some Properties of the Minimum Polynomial,” Lecture Notes in Computer Science, vol. 149, 1983.

I believe designs like hers [may even be byte based for efficiency] have been used in satellite TV encryption in the 1980s-1990s, but can't find the reference now.

There has been cryptanalysis showing such schemes may not be as strong as first thought.

Jovan Dj. Goliv, Mahmoud Salmasizadeh, Ed Dawson: Statistical Weakness of Multiplexed Sequences, Finite Fields and Their Applications 8(4):420-433, 2002.