I think the discussion about how much training the OP should have depends on what the OP is currently doing. Physically, there should be no reason why he can't finish these events with his current level of training ... he could have walked the last 25 km of that 300K and still made it with time to spare.
But in general, I find that if I'm not riding 1000 km/month or something very close to that, I struggle with the 300K+ distances. I need to be out there riding a lot in order to finish the randonnees comfortably. And I need to be riding long distances. One thing that helps get my head into the game is to do the Century-A-Month challenge ... I'm out there riding at least one century each month (and sometimes a longer distance). I get comfortable with what to eat, what to drink, my bicycle setup, the right clothing to wear, etc. etc. And in the past, many of my centuries in these CAM Challenges were solo. Me, my bicycle, and the road in front of me.