Hi,
You could try a lower frequency, like 10Hz or so, with a longer 'On' time, to allow the ringing to dampen by itself.
Now it could be stopped by the short 'on' time of the 1% of the 1kHz.
Did you see ringing nicely going down like in one of these pictures?
/g/TekScopes/album?id=254000This was a bad HV transformer en a good one for a 2235, but the principal is the same.
Good luck,
Leo