My answer is
(D). It took me 01:07.
"So" is one of the seven ("FANBOYS") coordinating conjunctions. The proper construction of a coordinating sentence is:
IC1 + Comma + FANBOYS + IC2. (IC stands for independent clause).
(A) Incorrect because "As ..." is a subordinate / dependent clause. We expect an IC.
(B) Incorrect. "Because ..." is a subordinate / dependent clause. We expect an IC.
A different view to eliminate (B) is that "because" and "so" are redundant.
(C) There are two issues.
1. "and" is one of the seven ("FANBOYS") coordinating conjunctions. The proper construction of a coordinating sentence is: IC1 + Comma + FANBOYS + IC2. The comma is missing before "and Jane".
2. ”to such a large degree that“ is frowned upon in GMAT. Use "so/such ... that..." instead.
(D) "As ..." is a subordinate / dependent clause. It is fine in this version because it is followed by an IC ("Jane was unable to understand the cause for his hysteria over the phone").
(E) Not a sentence. If we cross out the nonrestrictive relative clause ("who was unable to understand the cause for his hysteria over the phone"), it reads:
As John was so hysterical that he could not articulate well
and Jane, so she dropped everything at work and drove home.