Any country which struggles to appoint justices in a nonpartisan way will also struggle to assemble a panel in a nonpartisan way, I think.
Not totally immune to issues of partisanship, but at least somewhat insulated.
BTW, the original intent of the Electoral College in the United States was pretty similar to this. Electors were supposed to be independent actors exercising their independent judgement in selection of the president. It wasn't sustainable for long.
The electoral college is basically an appendix, except it was never a useful organ. It malfunctioned completely, right out of the gate.
Possibility to beat this deadlock: one party picking few candidates from the commission and OTHER party (parties) accepting one of them. Still can lead to "choose the lowest evil" and I can imagine Repiblicans not accepting anyone of Democrata were ruling.
Eg., members of the Supreme Court of the UK are appointed by the King on the advice of the Prime Minister. The Prime Minister is required by law to recommend the person nominated by an independent commission.
The selection must be made on merit, in accordance with the qualification criteria of section 25 of the Act, of someone not a member of the commission, ensuring that the judges will have between them knowledge and experience of all three of the UK's distinct legal systems, having regard to any guidance given by the Lord Chancellor, and of one person only.
https://en.wikipedia.org/wiki/Justice_of_the_Supreme_Court_o...
This seems to work fairly well and, although specific decisions are argued over as part of normal political discourse, it is generally seen as being non-partisan.
Ireland (which also has a common law legal system) has a similar setup, with the President appointing supreme court justices based on the recommendation of the government who, in turn, are advised by an independent panel. That advice is technically not legally binding, so this is in theory a less-strictly non-partisan system - but in practice it works out about the same.