How do I properly frame an opening to angle a through-wall air conditioner?
It's much easier to check that something is level than to check that something is 6 degrees or 1/4 inch higher.

Build it level. Then add a 1/4 inch strip of wood (a length of lath or trim) across the inside edge of the horizontal framing member.

You are correct that the sleeve will be sitting on two edges, the added trim strip and the outside edge of the exterior horizontal member. But the air conditiner is quite rigid and the sleeve sufficiently so to resist flex. The weight is not so great that the boards will be compressed or the machine flexed.