More info – just noticed it is screen-width dependent. Using Chromium, all is well for a narrow screen (or when using its mobile emulator, which also gives a narrow screen). But as the window is widened some lines are above the top of the screen and not visible – at the full width of my desktop monitor, 4 lines are not visible.
Yet more info: the described behavior occurs in Chrome (58.0, on 2 different boxes) and IE (11.0, I only have on 1 box), but for whatever reason NOT on Firefox (53.0, 2 different boxes).
Oops – now also had it occur in Firefox.
Hi there,
This isn’t specific to any particular theme. For example, if you try Twenty Seventeen, the same thing will happen with or without an image in your content.

If you use a theme that supports Jetpack’s Content Options, you don’t need to use the Read More feature. Instead, you can choose to let the theme show an excerpt. When a visitor clicks to continue reading, they’ll start at the top of the post.
A theme like Independent Publisher 2 might work as a similar theme for you:
https://wordpress.com/theme/independent-publisher-2/
You’ll need to have Jetpack installed for the Content Options feature.
Thanks much for your clarification. This seemed like such a deal-breaker that I assumed it was a bug specific to this theme – can’t imagine why anyone would use a “feature” like that if its going to hide content from the user on the jump! I feel somewhat locked into this theme since I’ve spent time making CSS modifications (but currently removed, so someone would not say they were affecting this problem). I do have jetpack installed so will see what I can do with “Custom Comment”. May try putting in a few <BR>s to see if that makes things usable. Or might use one of the plugins that removes the post “more” tag on the jump, so the full post is instead displayed (though since the banner image is so wide, would be better to instead jump to the top of the text – but guess I’d have to learn to develop in WS to do that!)
My solution: eventually I ended up (1) altering my style’s content-single.php to add a specified anchor tag just above the text lines (2) adding code in my style’s functions.php to alter the “more” tag such that it would instead go to the specified anchor tag. More info here:
https://wordpress.stackexchange.com/questions/272439/bad-read-more-behavior-trying-to-fix-by-inserting-tag/272941#272941