Unfortunately the extrusion and saw cut tolerances are +/- .015-.020. So you can see how that variance poses a problem.
This is the perfect way to illustrate, how the stacking of tolerances doesn't just apply to assemblies...
Technically, your extrusions & saw-cuts could all be in tolerance, but if all the tolerances fall on the plus, or minus side, then some other critical dimension - true position of a hole, from one of the exterior edges for example - could be off by a mile.
If you guys are seriously registering against saw-cut edges, and are expecting to hold tight-tolerance to the opposite side of the part, then you're blind, or crazy.
I've machined a lot of irregular forged parts in the past, which went through many operations/fixturings to finish the part. Just like in your example, there's a lot of variation on the incoming parts. You have to plan & anticipate these changes, and fixture the parts to allow for that.
I think dimensioning off a “floating edge” is fine as long as that surface is qualified during machining...just like you would in a VMC - If Z0. is the top of a saw-cut part you would “qualify” it by face milling to Z0. after ensuring the part is ALWAYS saw cut to at least .001 talker than the finished length.
I don't mean to single you out, but I can't ignore this. We may be splitting hairs here, but it's important.
You wouldn't dimension from this "floating edge" or sawed surface on a precision part. You dimension from a qualified surface - one that's been machined, or at least good condition from the bar.
(If the designer really did dimension from a saw-cut edge, then it's some manner of rough-ass part, that doesn't warrant any discussion on a precision machining forum... )
In your above example, if the top surface is saw cut, and you plan to machine this surface, then Z-zero is not the "top" of some rough sawn surface. It's at a carefully selected distance below where you expect that saw-cut surface to be. That is your datum/Z-work offset/qualified surface.
Maybe I'm in a bad mood today, but I can't believe the OP is having this much trouble understanding how varying stock allowances on incoming parts, can play havoc on tight-tolerance dimensions.
If there's tight-tolerance features that are being lost because of varying stock allowance on one or more edges, then you have to either 1-pre-machine the parts before the critical operation, 2- find every part by touching-off, or probing each part, or 3- change the fixturing to either clamp on a different surface, or compensate for any variations in stock allowance.
(IE, use a self-centering device for fixturing - a 3-jaw chuck is a perfect example.)