How to get clipboard to paste as PNG instead of TIFF

(2) If I copy-screen-to-clipboard (Opt-Cmd-Sh-4) and paste, I get a TIFF file.

Minor correction. The command to the clipboard is Ctrl-Cmd-Sh-4.

Once in the clipboard, the info is just raster data. It has no file format until you paste it into an app that can handle such data. Like Preview, Photoshop, etc. It's then up to you to save the image into the format you want.

For instance, once I do a screen shot to the clipboard, I can choose "New from Clipboard" in Preview. It displays the image in a new window. From there, I can do a "Save As" into a number of formats. But it isn't anything until then.

When you copy to clipboard, don't paste to desktop, paste to Preview and then save as whatever you want.