Okay, I made a couple breakthroughs in my quest...
First off, I realized the "Axiom 61" preset that comes with Sonar is worthless, unless you perhaps have the 2nd Generation model. I have the 1st Generation Axiom 61, and it seems like Cakewalk doesn't know nor care that M-Audio came out with 3 versions of the Axiom 61 to differentiate between the two. I'm just guessing it's the 2nd Generation since that one was on the market when X1 was being developed.
I Got The Transport Controls Working!
What I did was use the Axiom 49 ACT Controller preset (17) and used that as the basis of my setup. The Axiom 49 preset follows the 1st-Gen models is the exact same thing as the 61, the only difference being the number of keys. Using Enigma, I copied the #17 program to my Axiom 61's #1 slot.
I also followed some previous advice on this forum, and changed the MIDI Channel on the transport controls (to Ch 15 from no channel).
I also changed the settings on the REW and FF buttons:
For the REW button on Enigma:
MIDI CC: 146 (MIDI CC Toggle)
Ch: 15 Value1: 127
Value 2: 127 MIDI cc: 21
For the FF button:
MIDI CC: 146 (MIDI CC Toggle)
Ch: 15 Value1: 127
Value 2: 0 MIDI cc: 22
I also copied the MIDI parameters from the drum pads and applied them to the 8 buttons below the sliders. ...and then exported the settings to my keyboard.
The result: I was able to MIDI-learn the transport controls and operate them accordingly. The REW and FF buttons will go back/forward in time by pressing the button, and letting it go stops it. The buttons below the sliders, though, still do not work, nor does any of the shift functions (and I even reprogrammed it to a note-on command).
Using Cakewalk Generic Surface for Transport This is doable to an extent. You can program the PLAY, STOP and REC buttons on the Cakewalk Generic Surface setup panel, by doing the following:
1) Select "PLAY"/"STOP"/"REC"
2) Choose the "Controller" button; the value will be automatically set
3) IMPORTANT: Where it reads "Trigger Value" below the "MIDI Learn" button, enter "127."
4) Hit "MIDI Learn" and press the appropriate key
5) Repeat for the other buttons
6) Save preset and exit
One caveat is that the FF, REW and other buttons will not work. I'm sure there's a way to reprogram them, but haven't found a way.