"If possible, I would joint the board, then cut the strip."
THIS IS THE RIGHT WAY.
" is there something that make flat sawn better for the belly?"
Willie, I know I'm not PD, but to me the answer is actually there in the TBB's. Q.S. backing shows both summer and winter rings, making them less dense than the other cuts. But, since almost all woods are stronger in tension than compression, even those "weak" in tension, Q.S. backs have enough, even plenty, of tensile strength, if they have the essentially perfect grain required.
On the belly, the opposite is true. Removing 10-20% of the density, elasticity, and strength of the belly by making it QS (exposing more winter wood) then IS harmful. You might not notice with something like ipe, but with a "lesser" ring-porous wood, say black locust, that'll count a little.
That's my thinking.