Although not "part-time" as such if you can't get part-time or contract work there is another approach - mini-retirement.
The basic idea is this: these days you almost never work for one company for ever. So, work somewhere for, say, two or three years, then take a year out. If you ram down your expenses and save hard during your two or three year stint you should be able to afford to do this.
A mini-retirement can be of almost any duration you like. Before I went contracting I took several, ranging in length from three months to one year.
You need to plan carefully, but you will find the break of great benefit. My productivity after returning from a mini-retirement was breathtaking - I was like a completely different person.
If you want to stay with the same company discuss having a sabbatical - if they say "no" screw them - you are better off with another company.
Reading this comment thread and previous threads on HN I think there is a lesson here for HR departments in software companies - why are you running your engineers ragged when they would be so much more productive if they had more time off? I guess the old 40-hr week mentality has not quite caught up with modern developments...