I was following the "Jump to Content" link and then jumping to the link immediately following the upvote buttons in order to read the headlines, but today I realized that headlines have the lowest tab indices in the page right after the "Jump to Content" link, which makes browsing reddit with a screen reader much more comfortable and compensates for the lack of semantic headings, so I'm just leaving this here.

EDIT: In order for this to work, the caret must be on the "Jump to Content" link or on a headline. Pressing Control+Home on Windows moves the caret to the "beginning of the page which has the "Jump to Content" link. I couldn't be bothered to test this on my Mac.