I use a public folder so I don't know if this directly applies, but I only ever use "copy public link" once per game. After the first screenshot I will just look for the last picture I posted in the thread, right click -> Copy Image URL, paste it into the forum's image tags and edit the end of the filename, like this:
blahblahblahdl.dropbox.comblahblahblah/blahblahblahsecretfoldercodeblahblah/t0_1.jpg becomes
blahblahblahdl.dropbox.comblahblahblah/blahblahblahsecretfoldercodeblahblah/t0_2.jpg
blahblahblahdl.dropbox.comblahblahblah/blahblahblahsecretfoldercodeblahblah/t0_1.jpg becomes
blahblahblahdl.dropbox.comblahblahblah/blahblahblahsecretfoldercodeblahblah/t0_2.jpg