I think this will be a no - but just to check if you clever people have a wonder solution.
I have tried to change the level of a room after placement as it has gone in on the wrong level. The parameter is grayed out in the properties palette and dynamo says “this parameter is read only” when running the script below.
This looks like a similar issue I was having yesterday, i think it was where the parameter “Level” is defined twice within the family as built in parameters. ASSOCIATED_LEVEL_PARAM and LEVEL_PARAM from memory, but don’t quote me on that. It worked 50% of the time for me using the set.built-in.parameter node from #archi-lab worth a shot if nothing else