Yes, it is possible to use "ever since" with the present perfect. "Ever since" links two events, a cause event and something that is true from that point in time onward. This is actually ideal for the present perfect tense because one of the uses of the present perfect tense is to indicate that something which began in the past is still relevant in the present. An example of this use is your sentence:
"I always thought it was wrong, but ever since I read it, I've been more confused."
Using the present perfect with "ever since" shows that the speaker has been and is still confused by something which they read in the past.
With the past simple tense, as in your last sentence, it would be more appropriate to use "once" instead of "ever since". This is because "once" links a cause event with something that changed, but does not necessarily link to the present.
Once I did that, it stopped bothering me.
This sentence shows that the speaker was not bothered by "it" as soon as they did "that". It however gives not indication of whether this continues to be true in the present.
I saw your edit, if I understand right you meant to ask if it is possible to use "ever since" and present perfect without past simple, which would look something like:
"ever since" + present perfect + present
Ever since I have been pregnant I feel sick each morning.
The answer is no, this is not natural English. This structure may be encountered in informal English, but it is more natural to have the structure:
"ever since" + past simple + present perfect
Ever since I got pregnant I have felt sick each morning.
I haven't seen him
means, essentially, I have not seen him recently.
I didn't see him
means, I did not see him at some particular time.
When the "particular time" is recently, the two can be used almost interchangeably:
"Have you seen Bob around?"
"No, I haven't seen him."
"Did you see Bob just walk by here?"
"No, I didn't see him."
Other times, though, there are clearer dividing lines between when to use didn't see instead of haven't seen:
"Have you seen Mr. Hernandez go into Mrs. Olson's house?"
"Yes, I have seen that many times."
"On the night of the murder, did you see Mr. Hernandez go into Mrs. Olson's house?"
"Yes, I did see that."
The first question refers to a more open-ended span of time, while the second refers to a very specific time segment.
Best Answer
This is a good lesson that you can't always trust what native speakers write. Of course, sometimes it's impossible to know if the odd grammar is just slang or laziness.
You are correct, and the sentence should be:
to indicate an ongoing condition, or simply
to indicate a present condition.