I think you're correct in thinking it has been overwatered. I advise taking the stems that have broken off and using them to take cuttings. Detach or cut some healthy growth from above where it is soggy, dip the end in rooting hormone (Rootone is a reliable brand) and insert the end in a dampened mix of bark and potting soil. Place in a clear plastic bag perforated with holes so that it does not remain too wet, and keep it in bright light but out of the sun. In a few weeks roots will develop and you can pot it up. Be sure that there is plenty of bark for fast drainage in the potting soil so it does not become soggy again.
The existing plant may be brought back to life. Take it out of the pot and tease out and discard the soggy parts. Then repot in free draining soil (bark plus potting soil about 50:50). Water lightly and do not let the pot sit in water.