Soot exhaust leak

If I remember correctly, you have MTU 8v183's. If so, I would not run them on the hard like that with raw water pump disconnected. I think you'd be better off rotating them with the stop switch engaged to move oil around without letting the engines fire.

As for running them in the water. I'd rather run all of the engines on yachts I manage 30 minutes or more at the dock than 30 seconds. I run them for a good while until coolant temp rises to 140F or so, then run them up in Neutral to 1500 rpms for several minutes, then slowly bring them down and let them idle for 5 minutes after that, bump them in gear a few times. I haven't had any turbo issues, or any negative oil samples after doing this on many yachts for many years, and the exhaust temp gets over 400F and oil temp does get over 180-200F generally on the ones that show it (MANs).

You have to cover your investments. If the shop warrants the new injectors better, it may be worth serious consideration. IMO. A good injector shop that fixes them in hand is getting harder to find these days. I am spoiled to such a shop in Jax that services AND MATCHES all of my and my customers injectors. I get all the performance of new at reduced cost.
What I said above, new or used, they need to be popped and matched before installation

I do same same with my Mans at the dock. At 1000 rpm mine will come up to temp which helps eliminant moisture as well.

Same here I run my MANs as far as I can up to temp + pressures at the dock in the winter regularly.Just to spread the oil , prevent gaskets shrinking , and get heat into them .Yes a also leave them @ 1500 rpm for 15 mins in N . I think It’s nice for the impellers too ...to keep them fully flexible minimise cracking etc .
At tick over I turn the shafts too ....just a quick flick in gear that’s all .

My thoughts completely. Close off the air passages as discussed and wait for the spring. Then take it for a nice long cruise with fresh oil. Change the oil after 15-20 hours if you think you have junk in it. I think your inside for the winter, yes? That smoke inside the shed should go over well....

You can also put some damp rid in strategic locations. Maybe fabricate something using mesh rolled up in a sausage. Just thinking out loud here.

Make sure your shrink wrap is covering your air vents, too. So here in the NE for me, the last time I run the engines at the dock is early December, the first time the next season I run them is the end of March or beginning of April depending on the forecast. You can do this while you're shrink wrapped, just be cautious of fumes. The water temp here today is 42 degrees.

Are you storing down in FL or up here?

Where is the scavenged water going from your humidifier - the bilge?

Sorry. All my comments were based on a NE storage. I know nothing about properly storing in the south.