I shot off an email to verify the tolerances. They also want .0005" profile tolerance of the machined flat surfaces after welding so I think this maybe be a bit over-engineered. I believe the bores will have bearings pressed in so I can see the need for holding alignment but not to this degree.
We do parts not too dissimilar to this to comparable tolerances, though yours are certainly at the tight end.
We do it with weldments made here, too. Perpendicularity and parallelism in the tenths over 20" is not unheard of. Good stress relief and some indicators on the part when you're clamping it in place to ensure it doesn't move during setup. I know I couldn't do it. I'm happy to work with a great bunch of guys.
Every time a thread comes up with tight tolerances, people love to chime in like they're the only ones who know material moves when the temperature changes. Ignore it. There are standards for inspection for a reason. If your customer is going to check it at 20C, do the same. Make sure it has adequate soak time in the climate controlled room. If your customer is going to check it at 85F then find a way to make that happen, too, I guess. Hopefully they're sticking with standard and assuming 20C inspection environment.
You're certainly in a 'line boring' situation, though, unless your HMC table is just fucking phenomenal at re-positioning accurately. Maybe it's good enough. If you can get a bar through it from one setup and still hold the diameter, though, that'd be baller. Otherwise it might be an operation to sub out to a specialty shop.
Those ID grinders are neat as hell.