Within RAW, is there another way to qualify for the Treesinger's Plant Companions?
I'm aware of only one other option, the Supernaturalist Druid, which has the following feature:
Eldritch Botanist (Ex)
A supernaturalist can affect plants with mind-affecting effects she creates and with spells that normally affect animals. Any such spell that allows a Will save can instead be negated by the target plant with a successful Fortitude save at the same DC. She also can choose plant bond and green empathy, as a treesinger druid, in place of nature bond and wild empathy.
Bolding mine. It explicitly calls out the option of getting the plant bond feature from the Treesinger.
Paizo has not published any option for non-treesingers to gain plant companions. The closest available is the Grow Plant Creature feat, but that is not the same thing at all.