Depends on if there is scoring damage or just coked rings. Soaking the cylinders down for a week with marvel miracle oil and the block heater on might help. Chemical action is always better and faster at reasonable temperatures. Below about 70 degrees it can be almost inert.

I do not suspect scoring damage as the problem clears off or reduces as the pistons expand. I doubt there is any option to the soaking down first from what you post.

As it does sound like some of the rings may be glued into their fixed position or so sticky with gunk they cannot respond fast enough to seal well.

Also running for awhile after the soak down with a quart of marvel oil in the crankcase and one in the fuel tank may help as well. Diesel fuel does not seem to cut wvo residues. The mystery oil solvent base seems to. Fairly inexpensive to buy and add a little more to each cylinder once a day. Remember to roll the engine over well before innstalling the gllow plugs or injectors so you do not get a hydro lock.