As you can see here, deleted pages are still colored blue, so I think it would help to got them in red, like wikilinks.
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Yes, sadly the watchlist API doesn't offer that directly. I would have to do a database check for each page to see if it exists without making crosswatch slow if the replica databases are blocked or slow (I don't like adding many database dependencies as those will break it from time to time. It's possible, but it might end up to be a bit complicated.
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Maybe it helps, when you only check entrys of the watchlist which contains "moved" or "deleted"?
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Crosswatch seems unmaintained and inactive (see T269703). You may want to use https://meta.wikimedia.org/wiki/Special:GlobalWatchlist instead.