1
It's sort of a hassle, but copy paste a block of text with a title, subtitle, header 1,2,3,4, etc into your old doc, then one by one, select a bit of the text with the correct style, and "update Title to match", "update Header 1 to match"...
And finally, select all > Format > Paragraph Styles > Options > Use my default styles.
1
Since Jul. 25th 2019 it's actually possible to specify in which account to create the new file, exactly as you stated in your question.
From now on:
docs.new/1 - creates the file in your personal account
docs.new/2 - creates the file in your second account (if you're signed in)
That applies to all .new shortcut URLs, check the explainer video from Google.
1
One workaround solution that hasn't been mentioned here is using Google's "Version History" feature to name a specific version. While that won't exactly lock your file down, it will give you an easy way to restore the version you want if it ever changes.
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