Form my postmaster, I gathered that a stiff envelope can be sent as regualr first class envelope as long as it's not oversized. He said the non-machinable stamp is to be used when the envelope is not ridgid. For example, I send pwe mailings with a non-machineable stamp because I'm sending a single top loader in a number 10 envelope. That leaves a disparity in the firmness of the envelope because more than half the envelope is floppy. So it can't go through a machine.
But I have had some pwe's returned anyway as non-deliverable, because the address is bad. Even though I have the right address, I thing they were returned to me because the address was not in all caps. Or my handwriting is just bad. I did have one portage due, becasue they though the pwe was to thick, so they charged the package rate. It could be that my PO and the followign trail of processing centers are just being a pain.
As far as you not getting packages, it might be returned to sender which can add weeks delay and cost the sender double postage. Also some times you just have to wait. I have had one package take 6 months, or a pwe three weeks. And I think most stamps are being sold as forever stamps, so the rate increases shouldn't be a problem. You are also a must send first, which doubles the time it takes to get your cards. I hope this helps. Also, not all PO's do exactly the same thing, so I'm not questioning the method you presented.