Nice and clean blog :-)

From the point of view of a start-up, it only makes sense to go for a Fixed Priced model if they have clarity on the business logic of the development. If the business logic is still in the process of being figured out, then it would make more sense to do a thorough scenario analysis. But often for startups, the exact specifics remain to be chalked out and thus the requirements can never be completely frozen.

If the scenario analysis is not feasible, then a T&M approach would be much more beneficial. The only problem from the view of a start-up is that there is a risk if the solution vendor asks for/takes up more time than actually required.

A more hybrid model would be going the Agile way, wherein, the customer and the developers meet over and clarify the exact requirements. This not only increases the interactions of the developer and the client, but also gives the client multiple opportunities to foresee delays in deadlines and means to correct the deliverables if need be. Then we can even go ahead with module-wise payments as you have suggested.