MAPD is the fastest method I am aware of to get into the airlines with low or no time. The biggest drawback to the quick entry is the large expense. If you can have the govt. pay for a lot of it because you are in the service, then you are getting a great deal.
I do recommend Mesa Pilot Development, it is a good program.
Just be aware of what life at Mesa will be like, however, before you get started. Mesa pays low rates to their pilots (especially starting out) and treats them fairly poorly. Many of their pilots choose to quit or transfer to other regionals because they get fed up with the treatment. Not trying to scare you, but don't want you to be "surprised" after investing so much to get there.
There are BENEFITS to this however: poor treatment creates an environment where many choose not to stick around too long, this means much quicker upgrade times than at most regionals because of the high rate of attrition. If your goal is to eventually fly for a larger carrier (which I assume it is), and you are sure you can put up with the treatment for a few years, I'd say MAPD and Mesa are the best (quickest) way into the business.
Good luck