Regarding the straight-grain slab checking question:
I have super limited experience - a couple big black walnut logs and a few Wych Elm logs all slabbed between 6/4 and 12/4. The thickest ones checked least and dried truest, though I wasn't exactly limiting my drying time (Denver,Colorado, in an uninsulated attic through the heat of the summer 95* and the cold of the winter 10*). I second that they won't really dry until they're slabbed out - these had sat at the shop for two plus years and were green as the day they were cut when I slabbed them. My strategy is to let the slab do what it wants and "fix" the checks using George Nakashima style butterflies to prevent them from getting any wider. Other than that, there's an incredible amount of force in a big slab of wood. I talked to a guy who had built big steel frames to try to control warping in big slabs. The wood just bent the steel like it was pipe-cleaners! I still ended up with mostly workable material, though. Nothing really moved that much for me, so I think my strategy will remain "slab thick, finish to desired thickness".
I'm using an alaska mill as well, just fyi.