Here is my 2 cents for this SC problem.
(A) Although limited in their usefulness thus far, the company board’s several entrepreneurs
1: Their has not correct antecedent. Moreover, "limited in their usefulness" is modifying "the company board's entrepreneur s.
(B) Based on the limited usefulness thus far, several of the entrepreneurs on the company board
Dangling modifier error. "several of the entrepreneurs" are not based on something.
(C) With the limited usefulness thus far, several of the entrepreneurs on the company board
This is conspicuously wrong. prepositional phrase modifying the subject of attached clause. That is complete disaster.
(D) Despite the limited usefulness thus far, the several entrepreneurs on the company board
This option would have been much better if the main clause had been started with the program. However, the meaning is clear here. Sometime meaning over-weighs the grammar.
(E) While limited in usefulness thus far, the several entrepreneurs on the company board
While indicates the two clauses in same logical direction. But here we are seeing clear contrast in given problem statement.
In sum, D is winning option.
If anyone find correction to my logic, please let me know it.