you can only set the CS of the model during the creation. However changing the Model CS during "New" and using a projected coordinate system will not increase speed or accuracy, or make it possible to import more data, but it will limit the possible size of your model. The only reason to change the default settings is if you plan to work directly with the model's SQLite file outside Autodesk Infrastructure Modeler.
The User CS is used to display coordinates in the status bar and for any other CS display. You can set that to any coordinate system at any time without affecting how data is stored in the GIS database or displayed in the 3D model.
You do not need to change the CS even when all your data is stored in one different CS. Projecting to LL always does work lossless for AIM. In many cases, you will also be successful re-projecting data in an individual CS in AIM. But this depends on the CS you selected and on the input data as many CS have just a specific area which is valid. So here, you will face unexpected behavior in some cases.
You also cannot change the model CS afterwards, so once you run into such an problem, rebuilding the model may become necessary. Therefore we suggest not to change LL if you have no intend to work on the SQLite file directly or of cause policies. That way you will stay flexible for whatever data you will add in future.
When I try to publish a part of the project, I get the following error
These boundaries do not overlap with the defined boundaries of the coordinate system of the model. Bounds must be in the following range:
[82418.6; -928 519] - [917 581; 9.99796e +06]
How to cure it?
Looking at your numbers I assume you model has not been created in LL? If that is true this may exactly be an error due to the limited valid size of a projected CS. How have you chosen the extent of the scenario manually by the extent tool or chosen the entire model? If the latter you can try to publish a smaller area you are interested so you may get around rebuilding the model.