Is there a cheap alternative to AVRs that can run the .Net Micro Framework?
No.  The price of a microcontroller running the .NET framework will always be greater than the price for a microcontroller with equivalent performance (or equivalent to the price of a micro with greater performance) which is programmed in assembly, C, or even using the Arduino tools.  

When buying a microcontroller for the .NET framework, you pay for small transistors, you pay for more transistors, you pay for complexity, you probably pay for licensing a core developed somewhere else, and, since you're paying for all that, most manufacturers imagine that you'll want to pay for higher pin-count packages since your die budget supports them.  If you did this in assembly or C, you could get equivalent performance and pay a lot less.

See also the following questions:   


Arduino / Processing versus .NET Micro Framework? Best language? Best hardware?
Microcontroller with Java API
What are the .NET Micro Framework ready systems available?
Is C++ suitable for embedded systems?


The first question in the list is very applicable to this question, it just discusses the suitability of the .NET micro framework as opposed to the pricing and programming which we're discussing here.

If you still want to use .NET, you think you can get acceptable performance out and you're going to be buying a significant number of parts (at least 1k, probably easier at 10k), you can do the same thing that the vendors of the FEZ parts do: Have it loaded at the factory. It costs somewhere in the region of a quarter apiece  to program large files like the one you'll be working with.