If the Derived Work includes material licensed under the GPL, You may
instead license the Derived Work under the GPL.

No version specified. Not if it is GPL or LGPL, GPL2 or GPL3, AGPL3 or whatsoever.
Once you relicense software from ANY GPL under copyleft-next you can relicense under any other GPL license? Would this transition path allow downgrading from say the much more strict AGPL3 to the less strict GPL2 or even LGPL2?