Cd/mp3 player was not playing all tunes burned to disk

Question

Got my Mojo workin'.
That's a TDK "Mojo" CD-MP3 Digital Jukebox.
Sit back and relax while I tell of my Grand Journey of Exploration. (There is a question below too.)
I had made a some iTunes playlists of MP3s, and decided to burn them on CD-R disks for my portable player. I had them all sorted by Artist and Album. The burn process seemed to go well, but when I loaded the first disk into the Mojo, it seemed to scan the entire disk and count all the tunes. It finished counting after it found all 193 titles. However, when I tried to play them, it would only play the first 26 tunes or so. (Another disk I had burned at the same time (different playlist) gave similar unsatisfactory results, something like 19 out of 186 tunes.) I knew the Mojo was not a current model, and thought maybe there was some weird file incompatibility thing going on.
I popped the disk into my son's CD/MP3 player ("Koss" brand), and it managed to find 30 or 40 of them. A bit better, but not perfect.
I tried it in my DVD player, and it was able to play all 193 tunes. In fact, it loaded and started playing quicker than I had ever seen it do before. It usually thrashes and whirs for an annoyingly long time.
The odd thing was that the Koss was able to play all 76 tunes on another disk I had burned over a year ago, on my wife's Mac, with a version of iTunes for Mac System 9.2. Unfortunately, those files were gone from her Mac so I couldn't see what the iTunes setup was. I was thinking maybe the newer version of iTunes had a bug or something.
Then I inspected the old and new disks in the Finder and noticed that the new disk had a bunch of folders with the Artists' names, and each artist folder had folders within them with Album names, and the tunes were inside those folders.
The old disk (which worked fine in the Mojo player) just had the MP3 files and no folders whatsoever. I knew I was onto something, but I couldn't figure out how to burn a folder-less MP3 disk from iTunes, as opposed to doing it manually via the Finder.
I searched Apple.com > Support > Discussions > iTunes for Mac > Importing & Burning in iTunes for Mac yet again, this time using "folders" for the search term, and up popped several threads where people wanted files organized by folders on disks:
http://discussions.apple.com/thread.jspa?messageID=1464192
http://discussions.apple.com/thread.jspa?messageID=1791538
http://discussions.apple.com/thread.jspa?messageID=781976
... which brought me to the document "iTunes: How to set the play order of songs on an MP3 CD", at http://docs.info.apple.com/article.html?artnum=60931
So, I removed the columns for "Artist" and "Album" names from the playlist, and burned it, et voila! it worked just fine in my Mojo, which plays all 193 tunes. (Too bad I didn't fix the ID3 tags beforehand.)
Now, for points:
I had the playlist sorted by Artist, and here are the first four titles (of 193)
Title ____________ Artist____________
Relative Ways ...And You Will Know Us By The Trail Of Dead
Mistakes & Regrets ...And You Will Know Us By The Trail Of Dead
Jubilation 20 Minute Loop
Queen of Pain Alkaline Trio
Muffin57 All Natural Lemon And Lime Flavors
... etc.
Then when I remove the "Artist" column so that it only shows the Titles, it resorts like this:
Title ____________
Blacken My Thumb
Buckler
After School Thunder
Futuristic Genitalia
Once In A Lifetime (Cul De Sac)
... etc.
This is not the same as it was, nor is it alphabetical by Title.
If I click on the Title column header of course, it is ordered alphabetically by title, like this:
Title ____________
(Do Not Feed The) Oyster
(Got My) Rock Pants On
3 Away
27
68
Adventures In Conversation
After School Thunder
Algorithm Of Desire
Alive and Amplified
... etc.
Other than dragging all 193 tunes, one at a time, in order manually, how can I keep the original play order by Artist, without creating folders on the burned CD?
There is talk of "Copy to Play Order" in the iTunes Help/Support files...
To use this command, Control-click one of the songs in the playlist,
and choose "Copy to Play Order" from the shortcut menu. Tip: These
steps also apply to a playlist you have reordered directly (by clicking
on one of the column headers like Artist or Album).
... but I don't see that option when I Control-click anything. The bottom menuitem in the popup menu is "Clear". Same results with Right-clicking.
300 MHz "Blue & White" G3   Mac OS X (10.4.7)   iTunes 6.0.5

Answer 1

Hmm. I see that the spaces have been chopped out in part of my first post, and it appears that I cannot edit it.
For clarity's sake, these are the Artists' names, in the partial listing for Ordered by Artist example in my previous post:
...And You Will Know Us By The Trail Of Dead
...And You Will Know Us By The Trail Of Dead
20 Minute Loop
Alkaline Trio
All Natural Lemon And Lime Flavors