Still strange.
I have an ft-890, basically same rig different cosmetics.
Oh and welcome to the forum.
10/12 may share the same LO.
I don't have my schematic in front of me.
But still if it does not oscillate when connected to a dummy load, it should not oscillate when connected to any other load.
Both VFO's make it oscillate? or only one? Have you tried this in CW mode without the mic connected? Just using the keyer?
The rig oscillates in receive mode or only after you transmit into the antenna?
Have you tried different filter setting?
Just trying to narrow down the possibilities of what could be causing it.
PS voltage regulated or is there a bad filter cap in the PS allowing some AC ripple to get in the rig?
You may try using a different PS or a battery for test purposes.