Thanks for all your replies. I now know for sure that there is no way to apply a new style to a list while retaining indent information.
I'm expert in inDesign, and there, you always have to have a separate style for each indent level. So that's not so surprising.
But I am surprised how fragile the indent levels are if you choose to use the multi-level lists method.
Final question - is there a way to find different indent levels in 'Advanced Find and Replace'? There are options under 'Advanced Find and Replace>Find Formatting' like 'Paragraph>Outline Level' and 'Paragraph>Indentation>Inside' but I could not get settings where these would match any of the list levels. Can they?