Both variants are correct.
No. 1 with 'würde' leading has the upside that it eases comprehension, plus it sounds a bit more poetic at least to my ears.
Note however that there is a referrence problem with 'er': as is, this 'er' refers to the same person that 'seinen' does.
Also, 'war gebunden worden' is technically correct, but unusual; 'wurde gebunden' was your choice when simply reporting.
EDIT: I shouldn't call it unusual, rather: wheter 'war gebunden worden' is correct or not depends on the context in which this information is given; namely, is it placed with a review?
Lastly, when replacing 'er' by the person who gagged the poor guy, 'müssen' looks to be the correct modality.
Ein Fetzen war über seinen Mund gebunden worden, damit der Entführer ihn nicht würde schreien hören müssen.