I second the compression test!
Easy way to see if you need a compression test is to just pull off the air hose from the turbo to the intake of the engine. I would pull it off right at the turbo since that will be the highest concentration of oil (If it is leaking from the turbo). If there is engine oil leaking from the turbo into the engine it will make it smoke. But you mention low power also. If this isn't timing then it could be damage / wear inside the cylinders. You mention it sounds like it is missing so I would think it might have internal problems. Hopefully it doesn't but if it does you will need to rebuild her. A cheap way to tell if you want to rebuild it (Or to see if you might be able to afford to rebuild it) would be to take off the oil filter and cut it open. If it has 'sparkely' stuff inside the rebuild might be very expensive. If there is no metal parts in there then hopefully it is a good candidate for a rebuild. All this test will cost you is a new filter. In this case I would buy the cheapest one I could find for a replacement as quality won't really matter where this engine is headed. Oh, most quick change oil places have a filter cutter that won't make any metal particles as it cuts open the filter. It looks like a large tubing cutter! Just be aware if you use a hack saw or cut off wheel you will be putting metal shavings in there that can make it hard to determine if they are from the inside of the engine or your cutting.
Let us know what you find. Hopefully it is an easy fix!

 

My 12v smokes a fair amount of blue when the engine is cold, but I run full synthetic.

It's a pretty common trait with Cummins to smoke a little bit of blue on a cold start up, but if you run synthetic oil it can be quite a bit more. Once the engine gets up to temperature and everything expands into place it stops smoking.

Does the engine still smoke after getting up to temperature? How does it feel to drive? Does it feel like it is hitting on all 6?