I think 'Martin Lottery' is certainly the correct phrase. I'd never trust anyone else to move machines for me unless I could do it myself. Big named brand movers are too expensive and the 'man with van' types often cost a bit more and I just don't trust they would have the know-how Martin does after years of moving games.
Case in point I've used Martin to move 6 of the 14 machines I've had in the past 4 years. The last move was extremely lucky, Martin was 30 minutes from the pickup point when he was called so he was able to get the game and he was passing me on the way to drop off another, so within 1 hour of initial contact the game was in his van, and 11 hours later was in my gamesroom, probably the fastest move I've had.
Then I've had times where the game I'm expecting has been with him for 2 weeks or more because he simply wasn't anywhere near me, due to other deliveries etc. The thing is if it in the back of his van, yeah okay its getting a bit of movement with the road but at least I know it is well strapped up and covered properly and there is no chance of any damage. I see horror stories on pinside because in the US, they are forced to use big carriers due to the long distances and often this leads to damage to in shipping, in fact some sellers refuse to use shipping services alltogether because they've had games damaged by them (don't go looking for the AC/DC
BIBLE that was in a shipping truck that rolled over, you will weep!).
Yeah it's a lottery, but I'd rather Martin was doing it than anyone else. Yeah it can be a pain trying to sort it all out, but I've never had problems with him and you always get your game. If you're in a rush though, unless your really lucky like I was don't expect it to be fast, but at least you have peace of mind your game will arrive as it left the previous owner.