If it's any consolation, I ruined a really nice and quite unique brush with my first attempted reknot. Despite what you think now, you will have learned from this ... if only that steaming is rarely successful.
Cutting the knot off close to the base and then drilling out the remaining stump really is the most effective method. Naturally, you kill the knot and will have to supply a replacement. As
@TobyC has raised, there are some handles that you can take apart, crack apart or cut cleanly to get the underside of the knot. With a little sanding, polishing and glue the handles can be made to go back as they were without much visual difference.
It's not an exact science.