Thanks to this thread, I've finally figured out the secret. Everyone saying that it's dead simple is, well... not lying at all. It really isn't worth your while to overthink things (though I did really like the idea of dying on top of it and being resurrected with it in hand. Idea for a new super unique?)
That said, back when I was still pondering 'HOW?', I was thinking there might've been clues squirreled away not in Doom RL, but in a certain other project of Kornel's that's up at Chaosforge (aka the one based off where DS is taken from). There aren't any (as far as I know), but hey, if the dev's are feeling particularly evil when they're doing the next build...