HP Photosmart Pro B8350 RUINS thick paper prints!!!

I've had success printing photos on all kinds of photo stock with the B8350, from 4"x6" up to 13"x19". However, today I needed to print postcards and it seems that the printer just won't handle the paper.

I'm using Avery 4.25"x5.5" pre-scored inkjet postcard stock. I have a PDF that has the postcard design 4-up, with a .25" border around each card. I tried loading the paper in the tray for printing, and the prints run fine until the last half inch of the paper when it seems that the rollers will no longer feed it out correctly. This results in the last half inch of the print being ruined by the paper coming out of the exit tray at an angle.

After numerous failures with that method, I tried using the rear manual feed. This time, not only did the same last-half-inch misfeed happen, but the print also started .25" too high so the cards were all shifted beyond the edge of the paper!

How is it possible to print on heavy/card stock with this printer without having the last bit of the paper misfeed? PLEASE help!