Turns out you'd need a U3 SD Card to get stable 4K video.

Samsung Pro Plus 128GB MicroSDXC Memory Card (MB-MD128DA/AM) https://www.amazon.com/dp/B01CO48M36/ref=cm_sw_r_cp_apa_hX.yybKG7BVHQ

I'm sure there are others, but I imagine most will be on the order of ~$100

The crucial stat is 30MB/s write speed or better... If there is currently such a thing.

The one I got will be fine for my purposes, but you'll need something faster.