Maybe it's obvious, but I find resizing the window much smaller helps a lot with the close eye contact thing. Slack's huddles are good for this — their UI seems to be designed to be a small thing in the corner while you're doing other stuff.

I also used to find it disconcerting watching some YouTubers film themselves with their face taking up the entire screen. I must have got used to that though as I've not noticed it in a while.