Better approach to online builder
This looks good to me. A nice use of space, Everything is very clear and easy to read, just a couple of problems:

Magic Numbers / Strings

You have a few of these dotted about, a couple of examples:

ctor.Body.Instructions[1].Operand = context.Request["A"];

I have no idea what A signifies here, nor why it should be the first instruction's operand. Swap A with a const that gives that string a name describing its purpose. You can probably do the same for 1 in this scenario too, unless A's purpose is only FirstInstructionOperandCode or something similar.

Commenting

Your comments don't add anything to your code. A lot of them just describe what you're doing, which any maintenance programmer can work out by reading the actual code. Instead you should use your comments to describe why you're doing something, particularly if it breaks from the expected norms.

The most egregious example is this:

// Clear existing response.
context.Response.Clear();


Structure

The Write New Response section could be refactored out into a separate method, but unless you're writing these responses elsewhere, it's probably not going to give you any significant gains.