Good advice above.
While in theory your idea may hold some ground, but in reality whats the point? Why not just have one mortgage and pay a higher amount. Sounds like you are trying to apply Dave Ramsey's snowball debt theory to a situation where it is totally unnecessary.
Food for thought...
One "strategy" mortgage payment that I like (and adhere to) is to take your standard mortgage payment and add on the principle that would be due the next month (make sure you add a note or someway to verify that the mortgage holder is applying it towards the principle and not interest).
This creates a steadily growing payment (snowballish if you will) and, with my situation, I will pay off my house in 15 yrs rather than 30 yrs. My initial payments are around 1150 (850 standard payment, plus next months principle of 300). By year 15 they will be around 1700 (850 standard payment, plus next months principle of 850), increasing about $5 per month throughout that time period. Also saves me about 54,000 in interest payments.
Update: If you convert the extra payments to present dollars and convert the payments saved to present dollars I will end up with a net of -7,000. Not a terrible loss considering I will be mortgage free.
(I am not an accountant or finance person, so my calcs could very well be wrong. If you care to review my spreadsheet with the calcs let me know).