You can regard them as cleft sentences for additional information.
Take the first sentence (with a little change/simplification) for example.
- 用があり広島へ行きました。 I went to Hiroshima for an engagement.
Then
can be unfolded as
- (私が広島へ行ったのは)仕方なくですね。 It was because I had no choice (that I went to Hiroshima).
In terms of 'sentences pattern', the following are the same.
- 昨日彼女に会いました。たまたまです。I met her yesterday. (It was) Just by chance.
- たまたま彼女に会いました。昨日(のこと)です。 I met her by chance. (And it was) Yesterday.
[Edit] 仕方なくです/仕方ないです
When the subject is I, these are not very different.
- 私は広島へ行きました。仕方なくですね/仕方ないですね。
Both essentially mean I had to go to Hiroshima. Grammatically, 仕方なく (implicitly) modifies 行きました while 仕方ない refers to the fact that the speaker went to Hiroshima.
On the other hand, when the subject is not first person:
- 彼は広島へ行きました。仕方なくですね/仕方ないですね。
Here 仕方なくですね means that he had no choice but to go. 仕方ないですね indicates the speaker's feeling towards his going to Hiroshima (In effect, There is nothing I can do about his going. Depending on the context, I understand he had to go or I have to do without him etc.).