So, for me, the solution to the eye-contact issue was--believe it or not--to avoid eye contact. Well--not completely avoid. What I did was to train myself to look in the direction of the other person, rather than making actual eye contact. That way, the (usually neurotypical) conversational partner can read my face and my eyes, but I'm not distracted by theirs. It's a good compromise that makes understanding and participating in conversation a lot less cognitively taxing.
I don't know whether this is useful for everybody. Probably not; autism is so very diverse! For me, it's the best solution because I get the most information from another person's speech rather than their body language; and I read whole-body posture better than I read facial expression. So, to get the most information, I need to concentrate on the speech and its inflections. I'm very fond of music and somewhat talented, so I use a lot of my knowledge about music to understand speech. Whole-body posture is also easier for me, maybe because it's slower and larger, or maybe because (feel free to laugh) I learned how to read body postures from my cats! So, if I face in their direction and concentrate on their speech, I get the optimum amount of information.
After all, the point of communication is to get information from Brain A to Brain B. What does it matter if your strategy is a bit atypical?