Yesterday, I rescued a very sad, overwatered begonia from a friend's house. I am wondering if anyone has advice on how to nurse it back to health. FYI, I live in the Pacific Northwest, and this time of year it is warm ish (60-75 degrees) and only humid in the morning.

Here are some photos before I go into my description:

When I found it, it was in a huge pot - easily 6 inches on either side of that little stem. The soil was drenched and the plant was obviously drowning. There was another stem in the pot that was brown and rotting. When I inspected the roots, I found that the green stem, while it has lost all of its leaves, is still firm and has some healthy roots. I discarded the brown stem and brushed as much of the wet soil as possible without damaging the healthy roots, and then repotted the healthy stem into a smaller pot with a mixture of potting soil and perlite. I have not watered it yet, as there was still some wet soil clinging to the root ball. The new, dry soil appears to be wicking away the excess moisture. I checked just now and the soil is still moist but not wet. I have placed it in a window where it will receive dappled sunlight through trees.

Do you think this plant might be able to survive? Does anyone have tips for saving an overwatered begonia?