Weren't you looking for a small neck a week or two ago?
There are ways to avoid cramping regardless of the neck you are using. Try practicing chords (all chords including and especially bar chords) without your thumb touching the neck at all. It will seem impossible at first, but you will find it can be done by a change in where your guitar balances against your body.
Also try playing bar chords (again prefereably with no thumb) but instead of using the muscles in your hand to get enough pressure, imagine your left arm is really heavy and wants to drop to the floor. Use your fretting fingers to "hang" onto the neck. There is some great info (and diagrams) on this in a book called "pumping nylon". The book is for classical players, but its all relevant. Classical guitars have high actions, wide string spacing and completely flat fretboards. Classical guitarists very often have bar chord shapes moving around the neck, with the 2nd,3rd and 4th fingers free to play melody on top of the bar chords. If you are in a music shop, flip thru it and you'll find the page with the diagrams.
Another way you can allieveiate cramping is to look closely at how hard you grip with not just your thumb, but your fingers too. Try starting by playing a few notes, but pressing only hard enough so that the notes "buzz" against the fret. Once you can do this, SLOWLY try playing a scale where every note is buzzing a little. Then, move on to chords and eventually bar chords. It will take a few days/weeks to get this working every time, but you will develop a lot more sensitivity in your left hand and be able to play light, fast, easily and most importantly...cramp free.
