1. Is this combination possible by RAW?
All other Incarnate spells (if they pass the question below) are castable, yet only Primal Summoners are screwed if they'd love to call Mogaru...
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2. Is using the extra slots to cast (10th-SL heightened) Incarnate spells RAW in the first place?
The text for the feat only refers "summoning" spells, unlike Master Summoner which also calls out "incarnate" spells too. Is this an oversight?
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Edit: Upon closer inspection, Summon Kaiju is a Rare spell; no wonder it worked clunky with the Summoner class. Even so, shouldn't it work well thematically, at the very least...?
The problem is that while you can get a 10th level slot for the ability, you don't actually have 10th level spots for any other purpose. You have no way to add Summon Kaiju to your repertoire as a result.