There are a few issues here.
You have some key signature changes that are on individual staves, and in some places they are inconsistent between the staves, i.e. a singer who is resting in a section doesn’t have a key sig change at all. Change to Galley view, delete the key signatures from each staff and create a new “system” key signature.
In some places the lengths of the bars don’t match the hidden time signatures. Some of these bars have “explicit” rests (as if they were a pickup bar, though they are in the middle of the score) but in other places they seem to have been forced to contain a bar rest. In some cases the bar is longer than the given time signature, not shorter.
The voices in the import also look a bit odd. Some of the parts “randomly” switch between two voice, and near the end there are one or two isolated notes in a third voice (which is also used for the ossia bar). View / Note colour / Voice Colours will show that - but It might not matter, for the hidden staves problem.
It’s hard to find what is forcing the staves to display by just looking at the score, since what is displayed and hidden is also affected by the happenstance of where the system breaks occur. If you look at the individual parts, you can see which rests have not been consolidated into multirests, and that is probably a more accurate way to find the problems. Try selecting the “bar rests” and deleting them. Even a single bar between different time signatures should show as a one-bar multirest in the parts, unless something is stopping that.
It might be worth going to Edit / Preferences / MusicXML import and select the minimum set of options to get the notes and lyrics, but not force Dorico to follow all the formatting in the MusicXML.
I didn’t do the complete job of sorting this out, but if you can get rid of all the broken multirests and single-staff time signatures, that will probably fix most of the problem.
You could also try installing Musescore (free). It has good MusicXML support - if there are any errors in the MusicXML file, it will probably flag them. Just re-exporting the MusicXML from Musescore might give better results in Dorico if it cleans up some of the “features” in the MusicXML file.