As others have said, a lot will depend on your legislation since it may prescribe a particular way of arriving at the fractions for each co-inventor.
I thought about preparing a document, in which everybody writes down what they think they did, and how that part contributed to the invention
In germany certain questions are asked and particular answers ...
If any of the people involved have outstanding rights to the IP get a lawyer. That's not likely though.
If the patents were assigned to the university tech transfer organization and this is the kickback from them put it into a lab slush fund. Having money unencumbered by oversight will be useful to you. Use some of it to career boost the people who did the ...
(Expanding a bit on Buffy's answer)
Short answer: Use some math to make everyone happy.
This is actually a well-explained problem in economics for which there is a solution.
It is possible to mutually assess everyone's contribution, without anyone unfairly boosting their own contribution, so that the proceeds are distributed in a way that everyone is ...
Research has been done on questions like this.
The Cake Cutting Algorithm is about fair distribution of a resource. Perhaps you can apply it here, or a modification of it.
In fact, the current (April 2020) issue of Communications of the ACM has a new article that also gives background on the problem: Aziz and Mackenzie, A Bounded and Envy-Free Cake ...
Google translation of original:
First clarify what right the university can have. The balance is distributed. That is easy. Now, each invention can be quantified by the scope and number of claims. A list of the participants indicating their participation in each claim would be a starting point. This would be worth 50% of the patent. The rest of works, ...
How to equitably divide the economical benefits of a licensed patent among academic inventors?
First and foremost, you must abide by the law:
Establish who owns the patent, it mightn't be the inventors;
Establish how ownership is distributed, according to the law; and
You'll probably need to hire an attorney, since you may be ...