In the EU's case, multi-party competitive bidding, with the winner taking the prime slot and others being assigned modular chunks of the product, sounds attractive.

Specifically, with the stipulation that results would be used as a criteria in future bids.

tl;dr -- Use the pyramid league system (e.g. from football) with promotion and relegation to efficiently create industry competition. Fuck up too many projects, down the pyramid you go.

From past failures the 2 things I want to be addressed are: 1) Have a proper procurement agency with actual experts at the helm, they are the "customer", they hand over the bids, they measure success, they should of course listen to end users. 2) Shield the project from petty internal politics. While I understand that political interference is inevitable, especially if you get public funding. The top priority is to have a good alternative to existing software in these 3 categories I defined. Not yet another job program/kickback to politically well connected entities.

At stake: huge amounts of money

Naturally, people will go to great lengths to try and obtain that, by influencing the key decision makers.

So you put in a layer above the decision makers.

So they influence the layer above the decision makers.

Repeat-repeat.

The only true defense against corruption, at scale, is competition. Because then everyone tries to knife each other in the back, and it generally zero-sums.