Colin,
The developers of TextEdit chose many years ago to hard-code that center screen, new document location into the application. Because of the first sentence, it does not preserve document window location data in any .plist.
It will be like pulling teeth to get Apple to change this annoying oversight. You can send the macOS product team feedback though.
The following AppleScript will open a new TextEdit document, each time it is run, and force the document location to the upper-left side of the screen. On El Capitan, documents will overlay one another, and the ⌘+` keyboard shortcut can cycle among them. On High SIerra, the previous sentence still applies, or one can simply select Window menu : Merge all Documents, and have open document tabs in a forced upper-left TextEdit window.
-- TE.applescript
-- Launches TextEdit and immediately snaps default opened window location to upper-left corner.
-- VikingOSX, 2018-06-01, Apple Support Communities
tell application "TextEdit"
launch
make new document
tell front window to set its bounds to {0, 0, 600, 1100}
end tell
