Sentence Correction

From OG 12 SC 69:
Once they had seen the report from the medical
examiner, the investigators did not doubt whether
the body recovered from the river was the man who
had attempted to escape from the state prison.
(A) did not doubt whether the body recovered from
the river was
(B) have no doubt whether the body recovered
from the river was
(C) had not doubted that the body recovered from
the river was
(D) have no doubt whether the body recovered
from the river was that of
(E) had no doubt that the body recovered from the
river was that of

Can someone explain how to pick between D and E?

[spoiler]
My source of uncertainty is in Split #1. Can someone explain please, preferably with examples?

Split 1) HAD no doubt versus HAVE no doubt
Why is HAD necessary in the tense if the explanation provided says "Once X HAD HAPPENED, then Y HAPPENED"? Y's verb does not have "HAD". I am unclear on this point.

Split 2) was versus that of
That of is required because body needs to be compared to the body of the man and not the man itself
[/spoiler]

[spoiler]
OA is E
Explanation:
As it is used in the opening clause, the past
perfect verb tense indicates that an action in the
past was completed before another action in the
past: Once x had happened, then y happened. To
maintain proper verb sequence, the verb in the
main clause must therefore be in the simple past
tense. When doubt is used in a negative context
such as there is no doubt or he does not doubt, it
should be followed by that. A dead body cannot be
a man; the body is that of a man.

A Whether should be that; the body is that of a
man.
B Incorrect use of present verb have instead of
had; whether should be that; the body is that
of a man.
C Incorrect use of past-perfect verb had not
doubted instead of did not doubt; the body is
that of a man.
D Incorrect use of present verb have instead of
had; whether should be that.
E Correct. In this sentence, had no doubt is the
proper tense and is correctly followed by
that; that of is used to refer to the body of a
man.
Th e correct answer is E.
[/spoiler]