Immediate update: Apparently, I just had to launch Project Cappuccino again. It seems I hadn't touched it since the second-to-last update, so maybe the game wasn't "reinitialized" yet? In any case, without even closing SLK, just launching PC and reloading the Lock N Lewd page unlocked the cross-game feature. I'm leaving this thread for posterity, since I wasn't able to find anything on the topic myself when I was looking into it.