Add startup (maintenance) mode
Write and update a /wp-content/maintenance.php file during the core/plugin/theme/language update and install steps; and run those steps in a background process, while the FastCGI server starts-up ASAP.
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Ensure writing said file works as intended; returns 503 and content
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Background install steps à la wp-cron
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Set caching headers to disable caching?
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Build a page including a spinner and self-updating mechanism (meta-redirect?) 
Edited  by Dom Sekotill