We just wanted nothing more than to move the project forward smoothly, but a quarter of the principal sponsors raised objections to it and even tried to withdraw from it at the last minute.
We really wanted nothing more than to move forward with the project smoothly, but a quarter of the principal sponsors raised objections with our plan and even tried to withdraw from the project at the last minute.
Using "just" is redundant when paired with the phrase "nothing more than", as they mean the same thing. You could use either of them, or replace it all with 'only' or 'simply', or anything else similar, but there is no purpose to combining any of them outside of wordplay. I've assumed you were using "just" for extra emphasis, so I swapped it for "really" as that works better here.
Using "it" requires the context for what it is to be clear. With how you worded this, the only thing you could be referring to throughout is the project. This doesn't make sense for the sponsors to raise objections about when they already decided to back it though, so I'm guessing they raised objections about how you planned to complete the project instead, hence swapping the first "it" to "plan". However, this now means any future "it" would be talking about the plan instead of the project, so you also have to change the second "it" to clarify that you're talking about the project again.
5 juni 2023
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We wanted nothing more than to move the project forward, but a quarter of the principal sponsors raised objections and tried to withdraw at the last minute.
I cut out a few "filler" words to make it more concise! The other suggestions are great, too. This would constitute a more simple version of what you wrote.
6 juni 2023
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We wanted nothing more than for the project to go ahead smoothly, but a quarter of the major sponsors objected and even tried to back out at the last minute.
5 juni 2023
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