The first one is correct but the second one is unnatural.
It is because -(으)ㄴ 듯이 creates a clause of the surrounding situation while -났듯이 just brings up a similar case for comparison. Since 나를 쳐다보았다 is a concrete action of the moment, you need a similar dependent clause which describes a (seemingly) real situation.
More generally, -(으)ㄴ 듯이, -는 듯이, and -(으)ㄹ 듯이 create a situational clause of appropriate tense which directly affects the main clause, like having done something, doing something, or something suppositional, hypothetical or about to happen. This construct is much like "as if" in English which gives a direct description (which could be hypothetical, conjecturing, or even real) of the main clause.
-듯이 and -ㅆ듯이 create a clause which only serves as a basis of comparison rather than an accompanying situation (so it is always much less important than the other case of 듯이). You can think of it as "like / as" clause which describes the main one by giving an example.
Examples of -(으)ㄴ / 는 / (으)ㄹ 듯이 (듯 is a bound noun, and 듯이 creates an adverbial clause indicating a supposed or real situation for the main clause)
- 화가 난 듯이 나를 쳐다보았다 = Looked at me as if they were angry.
- 중요한 일이라도 하는 듯이 심각하다 = Looks serious as if doing something important.
- 뛸 듯이 기뻐했다 = Was so elated as to jump in the air.
(This -(으)ㄹ describes a possibility rather than the future)
Examples of 듯이 as verb ending creating a clause to compare the main clause with.
- 남이 너를 도와줬듯이 너도 남을 도와야 한다 = Just like others have helped you, you should help them too.
- 게(가) 눈 감추듯이 = The way a crab retracts (its eyes) into its shell (idiomatic expression describing doing something hastily)
- (future form of 듯이 would be -(으)ㄹ 것이듯이 (e.g. 할 것이듯이) but such constructs would be very rare since something that has not happened yet can't serve as a comparison)