aod won't shift past 3k

Don't think so. Did the "shop" adjust the cable to factory specs, or did you have them pull it out/stretch it? When I was with the ex and I stretched out her cable, I got it to shift @4,300-4,500 rpm w.o.t.
 
Bull. Have him show you how to adjust it. This way you can bring it up a bit higher on your own, to your liking. Obviously, don't stretch it ALL the way out as eventually, you could indeed hurt the trans internally over time..
 
It should shift at wot at 4.500 or above, depending on what the car is. Different model and year cars have different governors in the tail shaft that control the max rpm it will allow it to shift at with the TV cable set at the max setting. The Thunderbirds and Mark VII had the lowest one, around 4500 rpms, while certain Mustangs had ones that would allow 5000+ rpm shifts. With the car fully warmed up, in OD position and normal gears, it should shift into OD at light throttle around 40-45 MPH. If it is shifting before that, it confirms the TV cable needs to be slightly tighter. It is much better to have it slightly tight than a little loose.