This is something you can hear quite often about Project Management Techniques: they can solve problems, especially “not measurable” aspects of a project.
I see a basic problem here: how can you manage something you don’t know?
It is not a technique problem, for techniques can’t be a solution for basic problems.
Things are measurable = you know what you want (the product), therefore you have defined all that you need to obtain such product.
This is the first thing you need to do: define exactly what you want (i.e., the product), so that you can organize things.
Mind, a product can be an event, just to give an example.
If one is not operating this way, he/she is not doing project management; besides, he/she is probably going to get a mess.
I would advise you this link: even if it is an historical article, it is very enlightening, in particular the “Napoleon was a Project Manager” chapter.
What should you do?
1) I remind everyone of the common goal; they must reach a goal, therefore they should try to understand each other.
One can do whatever he/she wants, he/she will never obtain much unless they understand they need the will to work together without paying attention to cultural details.
2) In general terms, a homogeneous team is going to reach better results; I know this is going to sound out-of-the-main-flow but that is the truth.
Nowadays, diversity is a must; nonetheless, it creates problems, no way.
One may tell people how wonderful working with other cultures is, but in some weeks at most problems will arise between people.
For instance, take the habit of not using handkerchiefs (in thoser cultures, it would be disrespectful): people understand the real meaning, nonetheless there is always someone who feel “disturbed”. Obviously, the vice versa is true. The sum of a lot of little things is usually going to create unseen tensions.
Therefore, you should constantly be alert: immediately deal with signs of cultural misunderstanding.
In my opinion, assessment tools have a very bad impact.
If you are to decide and let a tool decide on your behalf instead, your people will get a bad impression, especially if the tool comes from other firms.
On the other hand, if you really need a tool to identify possible leaders in your organization …
Example: a tool deciding a person could get blocked in decisional environments. Try to guess? That person did practice “extreme sports”, i.e, he/she would have been dead had that been true. Nonetheless, he/she experienced problems in that occasion.