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Consider these:
[A] 僕はいい仕事があったら美智子さんと結婚出来ただろうに
[B] 僕はいい仕事があったら美智子さんと結婚出来たのに
Is に in [A] related to the case particle に?
Is のに in [B] related to the use of のに as a conjunction in mid-sentence?
Is it possible that their sentence ending usage originates from elision? I.e.,
[A'] 僕はいい仕事があったら美智子さんと結婚出来ただろうに(Elided content)
[B'] 僕はいい仕事があったら美智子さんと結婚出来たのに(Elided content)
Or have I no choice but to learn them as another atomic concept?
The に in だろうに historically comes from the case particle に, but in present Japanese, it should be considered a different thing. (Many things in Japanese that look like a particle actually do come from particles. Even the conjunction が as in 食べてみたが、まずかった is originally the nominative case particle が.)
In both cases, the continuing part is elided as you correctly suspected.
僕はいい仕事があったら美智子さんと結婚出来ただろうに、(いい仕事がなかったために、結婚できなかった。)
僕はいい仕事があったら美智子さんと結婚出来たのに、(いい仕事がなかったために、結婚できなかった。)
The reason it is usually elided is because its content can be reconstructed from the remaining part. Because the condition is a counterfactual condition, the continuing part, which is the reality, is simply the negation of the remaining part. The reason the condition is counterfactual is due to the use of past tense in the consequent of it. Past tense is usually used for facts that already happened, and cannot be changed in normal circumstances. Putting a past tense for a conseqnent to a condition implies that you are referring to a situation that had not happened. It is similar to how the English subjunctive past can mean a counterfactual event of a present time.
I'm surprised it is hard to find an entry of に in the dictionary that can fit the usage.
But finally I found this which is under the entry of だろう:
（「だろうに」の形で）事実に反する仮想を述べる。
(In the form ofだろうに) Saying some supposition that is different from the facts
「もう少しがんばれば、何とかなっただろうに」
If (you) try a little harder, you should have (succeeded).
It seems that we can even treat だろうに as a whole phrase.
I didn't find a source which give an origin of this usage. However, I don't think it is related to the case particle, nor that it is form from elision.
For the final use of the のに, it does come from the the conjunction use(source).
1［接助］《準体助詞「の」＋接続助詞「に」から》活用語の連体形に付く。内容的に矛盾する二つの事柄を、意外・不服の気持ちを込めてつなげる意を表す。
(from 準体助詞「の」＋接続助詞「に」) Used after 連体形. To link two contradict statement, with a feeling of unexpectedness or unsatisfactory.
「東京は晴れなのに大阪は雨だ」Although it is sunny in Tokyo, it is raining in Osaka.
「九月だというのに真夏の暑さだ」Although it is September, it is as hot as in summer.2［終助］《1の文末用法から》活用語の連体形に付く。不平・不満・恨み・非難などの気持ちを表す。
(From 1 when used at the end of sentence) Used after 連体形. Showing feeling of dissatisfaction, disapproval, bitterness, accusation.
「これで幸せになれると思ったのに」(I) thought (I) could be happy after this.
I think this use of のに can be treated as the latter half of the sentence elided.
NOTE: The translation of explanations and examples are made by myself.
