I am the WoodGuarden man helping you sport solid wood!! I have found Sapele to be very stable. I truly prefer the 3 ply birch as pickguard wood. It is extremely durable, resists warpage and stains up very nice. You can get some with nice grain patterns and really make that jump out with the finish.
The only woods I find very difficult in the 1/8 inch thickness are Padauk and the harder woods like Wenge. Padauk is soft and will snap very easy if not careful. The Wenge is almost like petrified wood, tightening the screws down can be hairy..