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I have searched long and hard for a dictionary translation of "soft deadline"
to no avail. Google Ngram shows that it has peaked in popularity in the last
three decades, so it's relatively new. I think it comes from computer science.

In any case, does my translation follow? Any other ideas would be appreciated.

UPDATE

As requested in the comments, here is an example in which I would use this
"soft deadline" expression:

"The hotel has a hard deadline for releasing rooms for the conference, so we
should move our soft deadline for attendees back a week from that."
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word-choice words
It seems "hard deadline" can be translated to 厳しい締切. Would "soft deadline" then be translated as 厳しくない締切?
厳しい締切 sounds too literal for my taste to be honest (it has more of a "tight
deadline" feel to it than "hard") and 厳しくない締切 sounds even stranger.

I suppose you are having difficulty finding a decent translation because
culturally, a soft deadline is quite the oxymoron here (Dates and times are
black and white here; If 2:00 is on time, 1:59 is early and 2:01 is late).

I know it's not the best answer, but you're going to have to provide context
for which this phrase is used.
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締切 means usually the deadline for manuscripts and applications. I can't catch
the word " soft deadline" in Japanese. If I say the sentence like " soft
deadline" in Japanese, I say like 締切にうるさくない or 締切に厳しくない.

締切 don't be used in your example. I think 退出期限 is used in your example as the
deadline.
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「厳しい締切」 means "there is little time until the deadline", rather than "you must
strictly meet this deadline." The antonym of this is 「緩【ゆる】い締切」, which is more
like "there is much time until the deadline," than "rough/tentative deadline".

If you need a word for "rough/tentative deadline", you can use 「一応の締切」「大体の締切」
or 「仮の締切」. For example, when you're inviting people to a party, and want to
roughly estimate the number of people by this date.

> 会場の準備の都合上、10月15日を仮の締切としますが、その日までに予定が決まらない方も、別途ご相談ください。

「[一次締切](https://www.google.co.jp/search?q=%E4%B8%80%E6%AC%A1%E7%B7%A0%E5%88%87)」
sounds more formal. For example when you're recruiting new employees, and want
to indicate there may be a chance for applying the job after this deadline.

Expressions like 「柔らかい締切」 are simply weird.
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