"...  lawyers working on this case are not seeking to make climate change "Legally actionable" ..."  I have to hope that you're right, but unfortunately have no reason to think so.  :(

" ... simply asking the federal government to set a science-based greenhouse gas reduction target to achieve a stable climate ..."  Then they are asking the impossible.  The United States could disappear tomorrow and 3/4 of the global  CO2 emissions would still exist.   There is also the problem of how we define a "natural" or "stable" climate.  Over geologic time, sea levels have risen and fallen and atmospheric CO2 levels have varied far more than anything you or I will ever see in our lifetimes.  May as well petition the Government to change the law of gravity so we all weigh less.  :-/