OP,
I agree with your thinking - hiring a guide/porter in Lukla and doing a 14 day trek. This is considering your budget that is really slim.
The Jiri version doesn't seem viable. Only saving on flights and extending the duration by one week wouldn't make it cheaper. Per day yes, but not totally.
into-thin-air,
I believe the nature does what's needed. Peeled or unpeeled potato must be better when grown naturally fertilised, not in ammonium and superphosphate. As kids we used to bake potato in hot ashes, never washed them, even if sometimes the skin was gritty. In those times they were also grown in earth fertilised with cow dung. The nature takes care of the process and it doesn't make you sick. Today I'd call it ecological, by my own definition. In Nepal they still do it.

