We have similar concepts in the Mishna.
One is the exiled murderer who is not allowed to leave his city of refuge, even if the entire nation needs him.
See Makos פרק ב - משנה ז
וַאֲפִלּוּ יִשְׂרָאֵל צְרִיכִים לוֹ, וַאֲפִלּוּ שַׂר צְבָא יִשְׂרָאֵל כְּיוֹאָב בֶּן צְרוּיָה, אֵינוֹ יוֹצֵא מִשָּׁם לְעוֹלָם, שֶׁנֶּאֱמַר (במדבר לה) אֲשֶׁר נָס שָׁמָּה, שָׁם תְּהֵא דִירָתוֹ, שָׁם תְּהֵא מִיתָתוֹ, שָׁם תְּהֵא קְבוּרָתוֹ.
Since the Mishna chooses the Chief of Staff, we're talking about endangering all Jews if he's not allowed to leave his city of refuge to take charge at the battlefront.
Yet we see that it's too bad; if the Halacha is that he has to stay put, then everybody else may suffer as a consequence.
But maybe execution by Bet Din is more lenient? To answer that we have another Mishna in Arochin פרק א - משנה ד
הָאִשָּׁה שֶׁהִיא יוֹצְאָה לֵהָרֵג, אֵין מַמְתִּינִין לָהּ עַד שֶׁתֵּלֵד. יָשְׁבָה עַל הַמַּשְׁבֵּר , מַמְתִּינִין לָהּ עַד שֶׁתֵּלֵד.
A pregnant criminal is sent to her death immediately. We do not wait for her to give birth unless she's already in labor.
The reason we don't wait is called Inuy HaDin; once a criminal is sentenced we don't put them through the agony of waiting for their sentence to be executed (pun intended). The execution takes place on the same day as the sentencing. The only delay is the time it takes to walk from the Bet Din to the location of the execution.
Even though if we wait we will have saved another person's life, Inuy HaDin takes precedence.
Once she's in labor, the fetus is considered as being alive and killing her would mean that the executor is killing two people, so we have to wait. Until she's in labor the fetus is considered part of her; we kill her heart, lungs, hands and fetus. Halacha doesn't consider this as killing 2 people.
So even in Bet Din we see that we don't consider waiting in order to save lives when the Halacha is that the criminal must be executed - no matter how indispensable the person is.
The only solution would be to not sentence him in the first place.