Do you use the manual method (drag and drop items on the shuffle in iTunes), or do you have automatic syncing set up? I'll go with the automatic syncing, and also assume your shuffle is 3rd or 4th (current) gen. You can post back if the situation is different.
The playlist itself needs to be on the shuffle. You can check by looking at the shuffle's content list.
NOTE: If the iTunes sidebar (along left side of window) is not visible, from the menu bar, under View, select Show Sidebar.
Find the shuffle in the sidebar, under DEVICES. Click the small triangle to the left of the shuffle name to drop down its content list (indented below the shuffle). Any playlists that are on the shuffle should appear listed there.
If the playlist is there, you can click on it there, to see the list to the right. If the playlist is not there, you can post back for info on how to automatically sync one or more playlists to the shuffle.
On the shuffle, if you play songs from the default All Songs list, and the power switch is set to the play-in-order (middle) position, songs play in alphabetical order. You need to use VoiceOver to switch to the playlist. Even if you only have one playlist on the shuffle, the All Songs list is the default selection.
This document describes how to set up and use VoiceOver (VoiceOver is the substitute for not having a screen on a shuffle)
Once you are playing from the playlist (not the All Songs list), the songs should play in playlist order (when the power switch is set to the play-in-order position).
This helped me figure it out my issues which was the same as above. The stupid thing is that on my ipod I have stupid voiceover disabled but still have to select the play list with pushing the voice over button. Idiotic if you ask me. Also another completely stupid thing is anytime I connect the ipod to my computer I have to re-select the playlist using voice over after disconnecting so it doesn't remember what I had selected. Good thing this is for my kid and won't change often otherwise I'd go nuts over such an stupid setting.
As someone who loads only ONE playlist on the shuffle, and wants to play the songs in a distinct order, you are caught between the larger groups of shuffle users:
The largest group by far are customers who don't care that the shuffle can hold playlists. They just load their favorite songs, and have the shuffle "shuffle" the playback from the default All Songs list. It's named shuffle for a reason. I'm in this group, when it comes to using my shuffle.
The second (smaller) group are the "power user" customers who use the multiple playlists feature, and appreciate it. They don't put just one playlist on the shuffle; they have mutliple playlists on the shuffle. Some may have podcasts (which are played in order), or different sets of songs for different situations. So, being able to select a particular playlist (from multiple choices) using VoiceOver is a key feature.
So, the design choices for the shuffle are not "idiotic" or "stupid" for how the shuffle is used by most of its customers.
I use a single playlist on my shuffle but had an issue getting it to play songs in the correct order that I wanted (alphabetically by song). It was always playing alphabetically by artist.
I tried to change the order in the playlist then hit copy to play order but this did not work.
I accidentally realized that "music" was set to alphabetically by artist. So this must have been where it was grabbing the order from when I synced my shuffle.
I finally got it to work by changing the order to the way I wanted it in "music" first, then made sure that my playlist was also in the correct order. Then I hit copy to play order then synced and it worked.
But my real question is: WHY CAN'T APPLE DOCUMENT THEIR PRODUCTS SO THAT THE USER GROUP DOESN'T HAVE TO SUPPORT EACH OTHER.
NOTE: If you click on the (top) "header" row of the playlist, it sorts the list by that column heading (the column heading you clicked on). So, if you click on the Name column heading, the playlist is sorted by song name alphabetically. Click on it again to reverse the order. If you click on the Artist column heading, the list is sorted by artist name. Etc...
If you click on the left-most end of the header row, above the sequential column of numbers, the list is sorted by playlist order. Although there is no heading label there, when this column heading is selected as the sort order, you can manually move the songs around (by dragging) to change the playlist order.
If you have that playlist selected for syncing on the shuffle's Music screen, the order of songs on the playlist as seen in iTunes before syncing becomes the playlist order for that playlist on the shuffle. So, some of those steps you described may not be necessary. Just make the song order of the playlist as desired in iTunes, then sync the shuffle.