I did some calculations and wanted to come back here to share them, and also to restate my problem statement so it is more-clear.
Consider a person who is currently running/jogging about 12 miles per week on a 10 min/mi pace for a total of 2 hours of exercise spread out over 3-4 days. This person wants to transition from running to walking for various reasons but doesn't want to lose out on too many of the benefits of their current exercise program in exchange for the perceived benefits (e.g. less wear-and-tear on the joints, less money spent on shoes, more-flexible exercise schedules that don't require changing clothes or showering, things like that).
How much walking, distance and time, at a pace between 15 and 20 min/mile (3 to 4 mph) on a small-to-moderate incline so as not to break out into a deep sweat, would they need to do to reproduce most (preferably all) of the health benefits of 12 miles of running in 2 hours per week?
Method used for analysis: hold calories expended constant, but subtract BMR for the time spent exercising because I could be napping.

I looked at my weight when I started (226 lb) and my current goal weight (174 lb), and held my age and height and gender constant, and here is what I found (I used
http://thefitgirls.com/calories-burned-calculator.aspx for the cal/hour numbers and BMR numbers for the various paces of running and walking):
226lb
BMR: 2070/day, 87/hour
6.0mph run pace: (844/hour-87/hour)/6.0mi = 126/mi
4.0mph walk pace: (431/hour-87/hour)/4.0mi = 86/mi
3.5mph walk pace: (371/hour-87/hour)/3.5mi = 81/mi
3.0mph walk pace: (302/hour-87/hour)/3.0mi = 72/mi
174lb
BMR: 1746/day, 73/hour
6.0mph run pace: (713/hour-73/hour)/6.0mi = 107/mi
4.0mph walk pace: (364/hour-73/hour)/4.0mi = 73/mi
3.5mph walk pace: (313/hour-73/hour)/3.5mi = 69/mi
3.0mph walk pace: (254/hour-73/hour)/3.0mi = 60/mi
Starting with the 12 miles of running in 2 hours, I get 1512 calories at 226 lb and 1284 calories at 174 lb. The number of miles I need to walk at the various paces to get to that calorie expenditure is as follows:
4.0mph walk pace: 226lb--17.6mi/4.4hr ; 174lb--17.6mi/4.4hr
3.5mph walk pace: 226lb--18.7mi/5.3hr ; 174lb--18.6mi/5.3hr
3.0mph walk pace: 226lb--21.0mi/7.0hr ; 174lb--21.4mi/7.1hr
So, it looks like I would need about 18 to 20 miles of walking over a 5 to 6 hour time period per week to get to rough equivalency to the 12 miles of running in 2 hours.
That gives me a sense of the requirements, at least to get caloric expenditure equivalency, but now I'm wondering if caloric expenditure equivalency is the correct measure? Also, assuming I transition from running 12 miles a week to walking 18-20 miles a week, what should I expect in terms of overall health benefits, etc. and what might be better and what might be not as good?
I know one thing I'd miss is the endorphins... I really like post-run endorphin levels.