The Yor can't culture flip planets at this time, well not easily.
The problem is, the Yor can only get 3 influence modules on their influence starbases. They are "Diplomatic Outpost", "Foreign Relations Center", and "Interstellar Embassy". All together, they provide a measly +22 bonus. When compared to what can be built with all of modules, you get a bonus of +337.
That is over 15 times what the Yor can build!!!
If the Yor had access all 6 modules of the "Diplomatic Outpost" tree (all modules that are either the module itself, or required it to have been built at some point), they could build influence starbases with a bonus of +82. That would put them at just under 1/4 of the power that would be had with all the modules.
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I would like to hear what you guys think about this.