Do all the registrars you work with allow inside pushes during the 60 day transfer lock period? Or have you worked with any registrar that doesn’t allow you to push a domain name to another same registrar account during that time period?
There is no such thing as a push to another registrar. That is a transfer. For transfer to another registrar you must wait out the 60 day lock period.
Domains can usually be pushed to another account within the same registrar only with no waiting period.The 60 day lock does not apply here. Most, not all, registrars allow this.