All hope was not lost. We made a small offering to the dice gods, then raided the hardware cabinet. A couple of threaded rod coupling nuts and a battery powered label maker later, we once again were rolling for sheep.
Step 1: Getting the pile of parts together
It takes 20 minutes, and for each dice you need:
A threaded rod coupling nut - I used one for 5/8" rod. A coupling nut for 1/2" rod would work as well, I just wanted bigger. Check out your local decently equipped hardware store to find these guys - cost is around$1.50 to $2.50 each. Coupling nuts are your basic hexagon piece of metal and are 5 to 6 times longer than your standard hex nut, so it won't roll onto the end unless you really try at it.
A label maker - Small label makers have become popular and plentiful the last few years - you might have one in a closet somewhere. If you don't have a label maker, print or write out the numbers on a piece of paper and cover it over with some clear packing tape.
Some packing tape - this is the standard stuff that comes off a tape gun. Scotch tape would work but it's not as strong or sticky.
The coupling nut I used was a hair over 3/4" in diameter and a bit over 2" long. Hex diameters are usually measured flat side to flat side. It weighs in at 2.6oz, compared to a normal 16mm d6 dice at 0.1oz. Yes, it makes a distinct noise when it rolls.
This coupling nut came with some holes and cutouts in it. Probably to let water drain if it's left outside or something like that. I just took some packing tape and put it over the holes, then used a utility knife to trim it down so the edges where all on one "flat" side. Packing tape will give the label when you put it on a little extra support so it doesn't puncture.