simply preserving sessions across disconnect

I have a really simple use case for screen. I like to use PuTTY from
my Windows laptop to Linux because PuTTY is a very nice terminal
emulator. The only problem I have with this is that when the network
connection drops, as in when I move around with the laptop, the PuTTY
session disconnects and all my state is lost. This of course is where
screen comes in; I recently discovered it and it seems very likely to
solve my problem.

When I tell putty to use "screen -x -R" as the remote command it works
great for one terminal window; I can reconnect to the screen session
after disconnects. But my normal usage mode is to have a number of
putty windows open for work in different branches or on different
bugs, and with the above setting when I make a second putty session it
connects to the same screen window.

Bottom line, it's a very simpleminded use case; I want screen to do
nothing except preserve my sessions across disconnect. I.e. if I open
3 putty sessions I want 3 different shell prompts in 3 screen windows.
If I then reboot the laptop I want my first 3 putty sessions to
reconnect to those existing windows (not necessarily in any order). So
each putty session should attach to an existing-but-unconnected screen
window if available and create one if not. I have no need for any
advanced usage like switching screen windows within a putty session.

Can anyone tell me the combination of flags to make this work?

Thanks, and sorry if my terminology is not up to par.

AK