I use a cross needle meter, two of them one meter is between the radio and one meter is after the amp at this time when I put theFirst thought is not to check SWR with SSB. If your AM SWR is good then the rest is good too. You are adjusting to a frequency not a transmit mode.
To be honest I have never even heard of any body check SWR with SSB. If you did not
re-calibrate on SSB that would explain why the SSB SWR is double of the AM reading.
tuner in line it too has a meter (cross needle).
I always watch my meters when I Tx. watching for Bad Reflect, then I saw the swr, and went into caution mode.