Q:

Where to put 从头到尾 in a sentence?

我从头到尾把他的电影看了一遍。

我把他的电影从头到尾看了一遍。

Which of the two sentences above is more idiomatic?

A:

1.我 [从头到尾] 把他的电影看了一遍。

2.我把他的电影 [从头到尾] 看了一遍。

Both are idiomatic.
[从头到尾] is an adverbial phrase that can be placed before or after the object [他的电影]. Just like the two sentences above.
In either case, the adverbial phrase must be placed before the verb phrase [看了一遍]
#1 place the adverbial phrase before the object. It emphasizes the adverbial phrase [从头到尾](from start to finish) -- What do you do from start to finish?
#2 place the object before the adverbial phrase. It emphasizes the object [他的电影] (his movies) -- What do you do to his movies?

A:

我把他的电影从头到尾看了一遍。

Is more idiomatic. 从头到尾 applies to 电影

我从头到尾把他的电影看了一遍。

Here 从头到尾 applies to 我，which is strange.
Nevertheless, colloquially people can still understand both expressions equally well.

