OK. So I started with the tube for #6 and #8. I chucked up the reamer and, of course, it bit hard and spun the tube. Got it pulled and started working on how I could ream it outside the hole. Well, it looks like attempts to ream outside the hole are pretty much doomed because you're trying to hold something that is getting thinner and weaker and it also seems to reliably find a weak spot after a while and chew through the side.
Fail
So, after a few experiments I decided that I would hand turn the reamer backwards gently in the hole, pulling it up each time it started to grab, lubing it with cutting oil, pulling it out regularly to wipe the brass dust off the flutes. It got caught a couple times. It did actually move slightly up at one point. It also took over four very patient hours. But the tube for #5 and #7 is now reamed out and the head bolt installed. One down, three to go.
Reaming
Winning