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I am not talking about consequences, such as in "I can't find my wallet, I
must have lost it" in which case I think something like ~に違いない could be used.
Rather, I would like to know how to express that something "must be + adj"
because of some reason.

**Example 1:** _We must be strong_ (for example because the times are tough).

**Example 2:** _The transition must be harmonious/peaceful_

My guess is that some verb conjugated in the "なければならない" form should be used,
with the verb depending on the situation.

My attempts:

**Example 1:** _強くでいなければならない_.

**Example 2:** _推移は...に行わなければならない_.

Which makes me realize I also would like to know what's a good word for
"peacefully/harmoniously" in this case. Notice that here I'm thinking of an
abstract transition from one state to another such as could be changing a job
or habit, rather than a concrete physical transition.

Anyway, I am really not very confident that my attempts make sense (if they
are grammatically correct at all) so even though somehow I feel this is
probably something quite basic, I'd appreciate some help. Thank you.
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grammar adjectives dictionary
How to express that something "must be + adj" as in "we must be strong"?
I would think your understanding of grammar is correct.

I'd translate Example 2:

The transition must be harmonious/peaceful.

移行は(穏便に/平和的に)進めなければならない。

推移 is more commonly used as continuous change such as

There are no drastic fluctuations in that transition.

その推移には大幅な変動はない。 - Weblio Email例文集

Transition of world major stock price indices

世界の主要な株価指数の推移 - 経済産業省

移行 is used as:

a sudden transition from autocracy to democracy.

独裁制から民主制への急激な移行. - 研究社 新英和中辞典

Hope it helps.
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Example 1: We must be strong (for example because the times are tough).  
Example 2: The transition must be harmonious/peaceful

Example 1: You: 強くでいなければならない. Me: 我々は強くあらねばならない。  
Example 2: You: 推移は...に行わなければならない. Me: 移行は円滑｛えんかつ｝に/平和裏{へいわり}に行われなければならない。

### 注釈

  * 「平和裏な移行」、あるいは「平和裏に移行する」は transition と peaceful が併存するような場合のほぼ set phrase です。
  * **EDIT** jisho.orgで"harmonious"を調べました。「円滑｛えんかつ｝に」が「平和裏に」と同程度の重みのある表現です。  
ＯＰの質問にはありませんが、このような時によく使われる表現に「粛々｛しゅくしゅく｝と～する」というのがあります。菅内閣官房長官(Chif Cabinet
Secretary Suga)が記者会見でよく使う表現です。  
It is important for us to **calmly proceed with** preparations and implement
the shift according to schedule. (日本語：決まっているスケジュールに沿って、 **粛々と** 準備をし、 **粛々と**
実施に移していくということが重要であると思っております。)

  * **EDIT** 「強くあらねばならない」＝「強く **ある** （to be strong）」+「ねばならない」  
As for 「ねばならない」, visit jisho.org with ねばならない, then, jisho.org tells you
なければならない means "have to do; must; should; ought to", and ねばならない is the other
form of なければならない. ​
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> I would like to know how to express that something "must be + adj" because
> of some reason.  
>  Example 1: We must be strong (for example because the times are tough).  
>  Example 2: The transition must be harmonious/peaceful
>
> My guess is that some verb conjugated in the "なければならない" form should be used,
> with the verb depending on the situation.

Yes, we usually translate 'must' in that sense as なければならない. You can also say
なくてはいけない as less formal version, or for a little more colloquial version
なくては駄目｛だめ｝だ, and we also say in everyday conversation しないといけない, しなきゃいけない,
しなくちゃダメだ (might sound like chiding), しなくちゃ, しなきゃ, and etc. あらねばならない sounds a
little too eloquent or splendid though, this is good as well.

> Example 1: 強くでいなければならない.

It could be 強くなければならない, 強くなければいけない, 強くなくてはいけない, 強くなくてはダメだ, and etc.

> Example 2: 推移は...に行わなければならない.  
>  I also would like to know what's a good word for "peacefully/harmoniously"
> in this case. Notice that here I'm thinking of an abstract transition from
> one state to another such as could be changing a job or habit, rather than a
> concrete physical transition.

推移｛すいい｝ is used for such as changes in statistical numbers or something that
we don't control over or that happens as the result of our efforts. As already
answered, 移行｛いこう｝ or maybe 切り｛きり｝替え｛かえ｝ would also work especially if the
context is something like 'habit', and 平和裏｛へいわり｝ is the first one that comes
to me as well, and 平和的｛へいわてき｝に or 穏便｛おんびん｝に seem to be the literal
translations of harmonious/peaceful.

Dependng on the context, you might want to say 調和的｛ちょうわてき｝に, 調和を図｛はか｝りながら,
釣{つ}り合い｛あい｝を取｛と｝りながら. It could be 穏{おだ}やかに or 緩やかに｛ゆるやかに｝ for 'habit' like in
change in diet or lifestyle; 食生活｛しょくせいかつ｝の切り替えは穏やかに なされるべき／なすべき／するべき です.
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I think you can also use 〜{しか・ほか}ない ("there's nothing but 〜", "there's no
alternative besides 〜") for this.

>   * 強くいるしかない → There's nothing (else) we can do but be strong → We must be
> strong
>   * 移行は穏便に行う・進めるほかない → There's no alternative besides (a) peaceful
> transition → The transition must be peaceful
>

However, this gives the statement a more objective feel to it (at least to
me).
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Every answer so far seems to be missing this distinction.

> We must be strong because the times are tough.

In this case, you are effectively saying that we need to **become** stronger
than we are now. Therefore, 強く **なら** なくてはならない is as good as 強くなくてはならない。The
former has more emphasis on the "become" part but they are essentially the
same thing, because you feel we aren't strong enough.

That "must" is different from the following:

> Come on guys. We must be strong enough to cope with this kind of pressure.

In this case, you know that we are already strong enough. It's just that the
strength hasn't come to the surface yet. In this case, 強いはずだ would be good.

The following one

> The transition must be peaceful.

is different yet because we are talking about the future here. In this case,
you can still use the second option of the first example: 移行は平和的でなくてはならない。
But, because we are talking about our future action, it's more natural to talk
about the action: 移行は平和裏に **行わ** なくてはならない。
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