Your unloading is the way most of the old hand mills did it. However, the dogs usually were on a ratchet and didn't fall down to the bunks.
The problem with the practice is sometimes the dogs will pull out past the saw for the return gig. Manual dogs cannot have any play in them.
When I run a hand mill, I like the offbearer to put the dogs up and push them in. I always want my dogs above the saw.