According to the Ran, that the reason we dont say tayninan in gittin is because "ein isha mamono shel ba'ala", why then is there no taininan by an eved who is mamono of the adon? And if you say that an eved is somehow not mamono and merely issur then why does the Ran (like Tosfos) ask where igun is found by an eved to allow the kula of befanei lichtav by an eid echad. Really without any kula the echad should be ne'eman to say befanai by an eved because it is only in the parsha of issur and eid echad ne'eman b'issurin.
Kol Tuv!
Asher Korbl, New York, NY
The Chasam Sofer (Gitin 2a) explains that Kiyum is necessary when Beis Din need to take a person's property away from him, whereas in the case of a Get, we do not stop the woman from marrying since she has a Get in her hand. This is what the Ran means when he says that the woman is not the possession of her husband. The Ran then adds that we do not hold her back from marrying.
However, Rav Shmuel Rozovski (in Chidushei Reb Shmuel (1:5) not to be confused with Shiurei Reb Shmuel by the same author) says as you suggest, that since the monetary ownership of the Eved is only possible as long as there is a Kinyan Isur, if the Shichrur is valid for the Kinyan Isur, then there is no Chashash Ziyuf for the monetary ownership.
He does not discuss your question from the Ran about Igun, but I would suggest that the Ran holds that Eid Echad is not sufficient because it is against "Ischazeik". This means that since we have taken on until now that the Eved was an Eved we cannot change this relying on one witness alone even for Isur.
Dov Freedman