yes so you need to manage the eagle.scr file. you could make a script or ulp that say changes the name between 2 files (ie names one eagle.scr and one something else) and then call that script from within eagle to pick what "setting" you want.
regarding "close", from what i understand close closes whatever editor window it is called from. so my idea was that say you double click a .brd or open a project that leads to a .brd and a.sch opening normally. the .sch will open and then immediately call close, adn well, close. i tested that and it works fine. this leaves only the .brd open.
i read the rest of the thread and re concerns of accidentally saving the .brd which may screw f/b annotation, you could add something like this to the BRD: block. the idea would be to immediately save a temp copy of the .brd so you aren't even working on the actual .brd file paired with the .sch.
to do this you could try adding the following commands to the BRD: block of the eagle.scr
write temp.brd;
edit temp.brd;
so what this will do is as soon as the brd context is opened WRITE will act as a save as and save the board as "temp.brd". After write though the orginal .brd is still open in the editor, so calling edit temp.brd will make it so the new one you jsut saved is opened instead. if the sch is already closed then it should not save a temp.sch. from testing you might have to move teh entire SCH: block above the BRD: block in the eagle.scr to ensure that the schematic context commands are executed first (and thus .sch closes) before the BRD: commands execute (this will avoid eagle asking you if you also want to save the .sch when you WRITE the temp.brd).
i didnt do tons of testing but it seems to work. here is some screencap of relevant sections
i take no blame for anything ofc but if it does not work let me know. im on eagle 9.6.2 in windows 10. (consider making backups of all files involved, eagle.scr, whatever guinea pig project you will test on, etc before doing any mods)
