Perhaps you can weld an extention onto a modified hole saw. Have a hole saw cut on half, then have a piece of pipe of matching dia. and wall thickness welded in between your halved hole saw. Grind the welds down and ther you have it. This will need to be done by a qualified tool maker/welder and the grinding will have to be done on a lathe. Use a quality hole saw that has adequate wall thickness.

I do hope your post didn't have a typo and you did mean a 6" long log and not a 6' long log...